periodically forced double homoclinic loops to a dissipative saddle abstract in this paper we present a comprehensive theory on the dynamics of strange attractors in periodically perturbed second order differential equations assuming that the unperturbed equations have two homoclinic loops to a dissipative saddle fixed point we prove the existence of many complicated dynamical objects for a large class of non autonomous second order equations ranging from attractive quasi periodic torus to newhouse sinks and henon like attractors and to rank one attractors with srb measures and full stochastic behavior this theory enables us to apply rigorously many profound dynamics theories on non uniformly hyperbolic maps developed in the last forty years including the newhouse theory the theory of srb measures the theory of henon like attractors and the theory of rank one attractors to the analysis of the strange attractors in a periodically perturbed duffing equation

homoclinic tangencies and hyperbolicity for surface diffeomorphisms we prove here that in the complement of the closure of the hyperbolic surface diffeomorphisms the ones exhibiting a homoclinic tangency are c 1 dense this represents a step towards the global understanding of dynamics of surface diffeomorphisms

finite element analysis of a class of problems in finite elastoplasticity based on the thermodynamical theory of materials of type n abstract this paper describes a finite element approximation scheme for computing finite elastoplastic deformations of a hypothetical class of materials referred to as materials of type n kinematical descriptions of motion and strain rate and rotationally invariant stress rates measures appropriate for finite elastoplastic deformations are derived and the thermodynamical theory for materials of type n is briefly reviewed finite element approximations of the governing nonlinear equations are derived along with numerical algorithms for solving the associated discrete nonlinear system these new methods are applied to some representative plane strain problem including problems with unloading and reloading and the problem of upsetting of a partially constrained rectangular billet

maps close to identity and universal maps in the newhouse domain given an n dimensional c r diffeomorphism g its renormalized iteration is an iteration of g restricted to a certain n dimensional ball and taken in some c r coordinates in which the ball acquires radius 1 we show that for any r 1 the renormalized iterations of c r close to identity maps of an n dimensional unit ball b n n 2 form a residual set among all orientation preserving c r diffeomorphisms b n r n in other words any generic n dimensional dynamical phenomenon can be obtained by iterations of c r close to identity maps with the same dimension of the phase space as an application we show that any c r generic two dimensional map that belongs to the newhouse domain i e it has a so called wild hyperbolic set so it is not uniformly hyperbolic nor uniformly partially hyperbolic and that neither contracts nor expands areas is c r universal in the sense that its iterations after an appropriate coordinate transformation c r approximate every orientation preserving two dimensional diffeomorphism arbitrarily well in particular every such universal map has an infinite set of coexisting hyperbolic attractors and repellers

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

identification of nonlinear membership function for failure of structural material and its application to structural optimization abstract the purpose of this paper is the identification and application of fuzzy membership function for material failure the concept of evolutionary damage in continuum damage mechanics is related with the decision of material failure in fuzzy set theory the failure phenomenon has a fuzzy nature and the internal state variable which indicates the degree of damage in continuum damage mechanics can be thought as a fuzzy membership function for failure in the structural design of machines such as automobiles airplanes and ships the results of the numerical analysis based on continuum damage mechanics which are verified by the uniaxial tensile test are introduced to obtain the evolution of the damage variable from which the fuzzy membership function for failure can be derived an exponential type fuzzy membership function is proposed to represent the fuzziness of material failure from the results of the numerical analysis in this study an elastoviscoplastic isotropic damage model of an isotropic hardening material is introduced and the three bar truss problem is revisited with the proposed fuzzy membership function which is applied to structural optimization

abundance of strange attractors in 1976 he h non performed a numerical study of the family of diffeomorphisms of the plane ha b x y 1 ax2 y bx and detected for parameter values a l 4 b 0 3 what seemed to be a non trivial attractor with a highly intricate geometric structure this family has since then been the subject of intense research both numerical and theoretical but its dynamics is still far from being completely understood in particular one could not exclude the possibility that the attractor observed by h6non were just a periodic orbit with a very high period recently in a remarkable paper bc2 benedicks and carleson were able to show that this is not the case at least for a positive lebesgue measure set of parameter values near a 2 b o more precisely they showed that if b 0 is small enough then for a positive measure set of a values near a 2 the corresponding diffeomorphism ha b exhibits a strange attractor their argument is a very creative extension of the techniques they had previously developed in bull for the study of the quadratic family on the real line and no doubt it will be important for the understanding of several other situations of complicated nonhyperbolic dynamics when acquainted in 1985 with the work by benedicks and carleson then in progress palls suggested that one should in this context think of the h6non family as a particular although important model for the creation of a horseshoe and that the emphasis should be put on the occurrence of unfoldings of homoclinic tangencies he proposed that the correct setting for benedicks carleson s results is within this more general framework of homoclinic bifurcations and stated the following

membership function as an evaluation abstract after giving an overview of the different kinds of mathematical forms of the membership functions we extract the different demands and determine the rational class of the membership functions from the generalisation of our result we can determine it giving four parameters the internal a b the sharpness and the decision level we show the correspondence of this membership function to the zimmermann zysno model and using their empirical data we also test our mathematical model we also show the connections between the operators of the evaluation and membership functions which gives the generalisation of this concept in a more general form as a special case we can get a linear form

chaos and crises in more than two dimensions instituto de astronomi ayfi sica del espacio conicet casilla de correo 67 socursal 28 1428 buenos aires argentina received 23 december 1996 noisy chaotic trajectories with nite time lyapunov exponents that uctuate about zero are basicallyunshadowable s dawson c grebogi t sauer and j a yorke phys rev lett 73 1927 1994 this canoccur when periodic orbits with different numbers of unstable directions coexist inside the attractor thepresence of a he non type chaotic saddle i e a nonattracting chaotic set with a structure similar to that of thehe non attractor guarantees such coexistence in a persistent manner s p dawson phys rev lett 76 4348 1996 in this paper we describe how these sets appear naturally in maps of more than two dimensions howthey can be found and what crises they produce s1063 651x 97 13005 7 pacs number s 05 45 1b 05 40 1ji introduction

multi objective optimization of fuzzy structural systems it is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures since most practical structural design problems involve several often conflicting objectives to be considered a multi objective fuzzy programming method is outlined in this work the fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points a method of solving a fuzzy multi objective structural optimization problem using ordinary single objective programming techniques is presented the computational approach is illustrated with two numerical examples

generic diffeomorphisms with superexponential growth of number of periodic orbits let m be a smooth compact manifold of dimension at least 2 and diff r m be the space of c r smooth diffeomorphisms of m associate to each diffeomorphism f 2 diff r m the sequence pn f of the number of isolated periodic points for f of period n in this paper we exhibit an open set n in the space of diffeomorphisms diff r m such for a baire generic diffeomorphism f 2 n the number of periodic points pnf grows with a period n faster than any following sequence of numbers fangn2zc along a subsequence i e pn f a ni for some ni 1 with i 1 in the cases of surface diffeomorphisms i e dim m d 2 an open set n with a supergrowth of the number of periodic points is a newhouse domain a proof of the man result is based on the gontchenko shilnikov turaev theorem gst a complete proof of that theorem is also presented

alternating cluster estimation a new tool for clustering and function approximation many clustering models define good clusters as extrema of objective functions optimization of these models is often done using an alternating optimization ao algorithm driven by necessary conditions for local extrema we abandon the objective function model in favor of a generalized model called alternating cluster estimation ace ace uses an alternating iteration architecture but membership and prototype functions are selected directly by the user virtually every clustering model can be realized as an instance of ace out of a large variety of possible instances of non ao models we present two examples 1 an algorithm with a dynamically changing prototype function that extracts representative data and 2 a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions we illustrate these non ao instances on three problems a simple clustering of plane data where we show that creating an unmatched ace algorithm overcomes some problems of fuzzy c means fcm ao and possibilistic c means pcm ao b functional approximation by clustering on a simple artificial data set and c functional approximation on a 12 input 1 output real world data set ace models work pretty well in all three cases

dense heteroclinic tangencies near a bykov cycle abstract this article presents a mechanism for the coexistence of hyperbolic and non hyperbolic dynamics arising in a neighbourhood of a bykov cycle where trajectories turn in opposite directions near the two nodes we say that the nodes have different chirality we show that in the set of vector fields defined on a three dimensional manifold there is a class where tangencies of the invariant manifolds of two hyperbolic saddle foci occur densely the class is defined by the presence of the bykov cycle and by a condition on the parameters that determine the linear part of the vector field at the equilibria this has important consequences the global dynamics is persistently dominated by heteroclinic tangencies and by newhouse phenomena coexisting with hyperbolic dynamics arising from transversality the coexistence gives rise to linked suspensions of cantor sets with hyperbolic and non hyperbolic dynamics in contrast with the case where the nodes have the same chirality we illustrate our theory with an explicit example where tangencies arise in the unfolding of a symmetric vector field on the three dimensional sphere

shil nikov configurations in any generic unfolding of the nilpotent singularity of codimension three on r3 abstract we are interested in the dynamics arising in generic unfoldings of the nilpotent singularity of codimension three since shil nikov type homoclinic orbits make up the simplest scenario where very complicated dynamics for three dimensional vector fields can be shown the aim of this paper is to prove analytically their existence in any of such unfoldings

strange attractors in saddle node cycles prevalence and globality we consider parametrized families of diffeomorphisms bifurcating through the creation of critical saddle node cycles we show that they always exhibit henon like strange attractors for a set of parameter values with positive lebesgue density at the bifurcation value in open classes of such families the strange attractors are of global type their basins contain an a priori defined neighbourhood of the cycle furthermore the bifurcation parameter may also be a point of positive density of hyperbolic dynamics

optimal design of laminated composite plates in a fuzzy environment the present study focuses on a fuzzy optimization approach to the optimal design of simply supported laminated composite plates the goal is minimum weight design of the composite plates the design constraints are the magnitude of center displacement and lamina failure criteria a procedure of two level optimization in a fuzzy environment is presented and this procedure is applied to the design of laminated composite plates to consider the influences of fiber direction and thickness of each lamina separately it is shown that the membership function in the case of failure can be deduced from continuum damage mechanics the membership function for failure criteria is the function of the internal state variable for degree of damage in the continuum damage mechanics the modified weibull membership function is chosen to be used as a simple case of damage progression the finite element method is used to calculate the displacement of the plate and the stresses of each lamina the fuzzy optimization formulation as a max min problem is transformed into a classical one this classical optimization problem is solved using the augmented lagrange multiplier method with the quasi newton method two examples are solved to demonstrate the procedure from the results it is shown that optimal design of laminated composite plates is more useful in a fuzzy environment and the modified weibull membership function characterizes the fuzziness of failure nomenclature bi upper limit of the inequality constraint d fuzzy decision f x objective function f x fuzzy goal

strange attractors in periodically kicked limit cycles and hopf bifurcations we prove the emergence of chaotic behavior in the form of horseshoes and strange attractors with srb measures when certain simple dynamical systems are kicked at periodic time intervals the settings considered include limit cycles and stationary points undergoing hopf bifurcations

global bifurcations close to symmetry abstract heteroclinic cycles involving two saddle foci where the saddle foci share both invariant manifolds occur persistently in some symmetric differential equations on the 3 dimensional sphere we analyse the dynamics around this type of cycle in the case when trajectories near the two equilibria turn in the same direction around a 1 dimensional connection the saddle foci have the same chirality when part of the symmetry is broken the 2 dimensional invariant manifolds intersect transversely creating a heteroclinic network of bykov cycles we show that the proximity of symmetry creates heteroclinic tangencies that coexist with hyperbolic dynamics there are n pulse heteroclinic tangencies trajectories that follow the original cycle n times around before they arrive at the other node each n pulse heteroclinic tangency is accumulated by a sequence of n 1 pulse ones this coexists with the suspension of horseshoes defined on an infinite set of disjoint strips where the first return map is hyperbolic we also show how as the system approaches full symmetry the suspended horseshoes are destroyed creating regions with infinitely many attracting periodic solutions

strange attractors with one direction of instability we give simple conditions that guarantee for strongly dissipative maps the existence of strange attractors with a single direction of instability and certain controlled behaviors only the d 2 case is treated in this paper although our approach is by no means limited to two phase dimensions we develop a dynamical picture for the attractors in this class proving they have many of the statistical properties associated with chaos positive lyapunov exponents existence of srb measures and exponential decay of correlations other results include the geometry of fractal critical sets nonuniform hyperbolic behavior symbolic coding of orbits and formulas for topological entropy

combining historical and randomized controls for assessing trends in proportions abstract a statistical method for incorporating historical control data in the analysis of proportions is proposed and illustrated the method has as its extremes logistic regressions completely pooling and completely ignoring historical controls the degree of pooling used is determined by the variability from experiment to experiment in the control incidences the fit of historical control groups to an assumed normal logistic model is assessed using probability plotting techniques monte carlo studies evaluate the adequacy of the asymptotic approximation used sensitivity analyses show that results are insensitive to alternative priors the method is applied to several sets of tumor data from animal experiments

dynamics of homoclinic tangles in periodically perturbed second order equations we obtain a comprehensive description on the overall geometrical and dynamical structures of homoclinic tangles in periodically perturbed second order ordinary differential equations with dissipation let be the size of perturbation and be the entire homoclinic tangle we prove in particular that i for infinitely many disjoint open sets of contains nothing else but a horseshoe of infinitely many branches ii for infinitely many disjoint open sets of contains nothing else but one sink and one horseshoe of infinitely many branches and iii there are positive measure sets of so that admits strange attractors with sinai ruelle bowen measure we also use the equation d2qdt2 q2 dqdt q q2 q2sin t to illustrate how to apply our theory to the analysis and to the numerical simulations of a given equation

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

the collet eckmann condition for rational functions on the riemann sphere we show that the set of collet eckmann maps has positive lebesgue measure in the space of rational maps on the riemann sphere for any fixed degree d 2

persistent homoclinic tangencies in the he non family abstract homoclinic tangencies in the henon family f x y x 2 by x for the parameter values b 0 3 and 1 270 1 420 are investigated our main observation is that there exist three intervals comprising 93 percent of the values of the parameter such that for a dense set of parameter values in these intervals the henon family possesses a homoclinic tangency therefore one should expect long parameter intervals where the henon family is not structurally stable strong numerical support for this observation is provided

global generic dynamics close to symmetry abstract our object of study is the dynamics that arises in generic perturbations of an asymptotically stable heteroclinic cycle in s 3 the cycle involves two saddle foci of different type and is structurally stable within the class of z 2 z 2 symmetric vector fields the cycle contains a two dimensional connection that persists as a transverse intersection of invariant surfaces under symmetry breaking perturbations gradually breaking the symmetry in a two parameter family we get a wide range of dynamical behaviour an attracting periodic trajectory other heteroclinic trajectories homoclinic orbits n pulses suspended horseshoes and cascades of bifurcations of periodic trajectories near an unstable homoclinic cycle of shilnikov type we also show that generically the coexistence of linked homoclinic orbits at the two saddle foci has codimension 2 and takes place arbitrarily close to the symmetric cycle

on iterations of 1 ax 2 on 1 1 on etudie des iterations de f x a 1 ax u 2 1 x 1 ou a est un parametre dans l intervalle 0 2 on etablit la non existence de cycles attractifs on definit une partition on donne une estimation uniforme de la a derivee

sinai bowen ruelle measures for certain henon maps we study maps t a b 2 2 defined by t a b left x y right left 1 a x 2 y bx right 0 0

a note on the numerical analysis of material damage based on the theory of materials of type n abstract a generalization of the theory of materials of type n to continuum damage mechanics is presented then algorithms developed earlier by the authors for plasticity problems are extended and applied to the analysis of progressive damage of materials under large elastoplastic deformation results obtained by applying these methods to representative problems of metal forming are presented

hopf saddle node bifurcation for fixed points of 3d diffeomorphisms analysis of a resonance bubble the dynamics near a hopf saddle node bifurcation of fixed points of diffeomorphisms is analysed by means of a case study a two parameter model map g is constructed such that at the central bifurcation the derivative has two complex conjugate eigenvalues of modulus one and one real eigenvalue equal to 1 to investigate the effect of resonances the complex eigenvalues are selected to have a 1 5 resonance it is shown that near the origin of the parameter space the family g has two secondary hopf saddle node bifurcations of period five points a cone like structure exists in the neighbourhood formed by two surfaces of saddle node and a surface of hopf bifurcations quasi periodic bifurcations of an invariant circle forming a frayed boundary are numerically shown to occur in model g along such cantor like boundary an intricate bifurcation structure is detected near a 1 5 resonance gap subordinate quasi periodic bifurcations are found nearby suggesting the occurrence of a cascade of quasi periodic bifurcations c 2008 elsevier b v all rights reserved

from invariant curves to strange attractors we prove that simple mechanical systems when subjected to external periodic forcing can exhibit a surprisingly rich array of dynamical behaviors as parameters are varied in particular the existence of global strange attractors with fully stochastic properties is proved for a class of second order odes

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

on the dynamics of dominated splitting let f m m be a c 2 dieomorphism of a compact surface we give a complete description of the dynamics of any compact invariant set having dominated splitting in particular we prove a spectral decomposition theorem for the limit set l f under the assumption of dominated splitting moreover we describe all the bifurcations that these systems can exhibit and the dierent types of dynamics that could follow for small c r perturbations

periodic orbits for interval maps with sharp cusps abstract we study families of unimodal interval maps having a sharp cusp at a critical point we describe bifurcations and distribution of periodic orbits period adding for attracting periodic orbits is observed that is period k is followed by k 1 etc coexistence of attractors of successive periods as well as of an attracting fixed point and chaos occurs periodic orbits of various periods are grouped into bunches and occupy a relatively small part of the space

positive lyapunov exponents in families of one dimensional dynamical systems we give a generalization of jakobson s theorem ja and a precise estimate for the density of parameters corresponding to systems with absolutely continuous invariant measures

utilizing concentration response data from individual components to detect statistically significant departures from additivity in chemical mixtures the classical approach for detecting interactions in a combination of drugs or chemicals is that of the isobologram quantified and generalized by berenbaum 1981 advances il cancer research 35 269 335 in this formulation it is assumed that contours of constant response of the dose response surface are planar if the compounds do not interact building upon this approach this paper develops methodology for detecting and characterizing departures from additivity reflecting the local rather than global nature of departure from additivity this methodology only requires doseresponse data for the individual components and the specific combinations s of interest this is in contrast to the larger experiments required to estimate the multidimensional dose response surface for the combination procedures for incorporating data from multiple control groups are developed for a fixed effects model a random effects model and through use of a generalized estimating equations approach an example is given that illustrates the application of these techniques to the analysis of a mixture of polycyclic aromatic hydrocarbons found in kerosene soot

heteroclinic tangles in time periodic equations abstract in this paper we prove that when a heteroclinic loop is periodically perturbed three types of heteroclinic tangles are created and they compete in the space of where is a parameter representing the magnitude of the perturbations the three types are a transient heteroclinic tangles containing no gibbs measures b heteroclinic tangles dominated by sinks representing stable dynamical behavior and c heteroclinic tangles with strange attractors admitting srb measures representing chaos we also prove that as 0 the organization of the three types of heteroclinic tangles depends sensitively on the ratio of the unstable eigenvalues of the saddle fixed points of the heteroclinic connections the theory developed in this paper is explicitly applicable to the analysis of various specific differential equations and the results obtained are well beyond the capacity of the classical birkhoff melnikov smale method

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

dissipative homoclinic loops of two dimensional maps and strange attractors with one direction of instability we prove that when subjected to periodic forcing of the form p t d h x y c sin t certain two dimensional vector fields with dissipative homoclinic loops generate strange attractors with sinai ruelle bowen measures for a set of forcing parameters of positive lebesgue measure the proof extends ideas of afraimovich and shilnikov and applies the recent theory of rank 1 maps developed by wang and young we prove a general theorem and then apply this theorem to an explicit model a forced duffing equation of the form d 2 q

entropy and rotation intervals for circle maps near saddle node bifurcations abstract consider a one parameter family of c r endomorphisms f lambda of the circle suppose that f 0 is on the boundary of an interval of phase locking and that f lambda generically unfolds f 0 so that f lambda exhibits nontrivial behavior for lambda 0 we show that the topological entropy and the width of the rotation interval of f lambda satisfy certain scaling laws as lambda searrow 0 and give estimates for each of these characteristics these scalings depend only on f 0 not on the particular family f lambda which unfolds it

incorporating historical controls in testing for a trend in proportions abstract the testing of chemicals for carcinogenic activity in lifetime rodent bioassays has produced a large amount of data on a few strains of mice and rats because of the use of fixed protocols in repeated experiments the opportunity presents itself for using this historical data in the analysis of a current experiment what has been considered is the statistical incorporation of the historical control data into the current control group to increase the power of the test this is especially relevant when dealing with tumors of a rare type where the toxicologist will place great significance on their occurrence in a treatment group experimentally it is assumed that three groups of about 50 animals each are tested at two treatment levels and a control the response for each treatment group is assumed to be binomial further it is assumed that the probability of an animal with a tumor in the control group has a beta distribution that is determined from the historical control data several authors demp

hyperbolicity sinks and measure in one dimensional dynamics letf be ac2 map of the circle or the interval and let f denote the complement of the basins of attraction of the attracting periodic orbits we prove that f is a hyperbolic expanding set if and obviously only if every periodic point is hyperbolic and f doesn t contain the critical point this is the real one dimensional version of fatou s hyperbolicity criteria for holomorphic endomorphisms of the riemann sphere we also explore other applications of the techniques used for the result above proving for instance that for everyc2 immersionf of the circle i e a map of the circle onto itself without critical points either its julia set has measure zero or it is the whole circle and thenf is ergodic i e positively invariant borel sets have zero or full measure

critical saddle node bifurcations and morse smale maps abstract we study the saddle node bifurcation in diffeomorphisms with a critical homoclinic orbit to the saddle node point in a typical family f of diffeomorphisms that undergoes a saddle node bifurcation at 0 the diffeomorphisms possibly after reparameterization for 0 have two periodic points which coalesce for 0 and then disappear for 0 if the saddle node points has a critical homoclinic orbit it is known that complicated dynamics can occur for 0 we show that there are families such that for 0 there are parameter values arbitrarily close to 0 for which the map is morse smale such parameter values are shown to have positive frequency at 0 in the process we show that the boundary of the set of morse smale diffeomorphisms possesses comb like structures we also show that there are other families unfolding a saddle node for which there are no morse smale maps for 0 these results rely heavily on projecting to circle endomorphisms we conclude with some numerical results from such maps

how often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency abstract here we study an amazing phenomenon discovered by newhouse s newhouse non density of axiom a a on s 2 in proc sympos pure math vol 14 amer math soc 1970 pp 191 202 s newhouse diffeomorphisms with infinitely many sinks topology 13 1974 9 18 s newhouse the abundance of wild hyperbolic sets and nonsmooth stable sets of diffeomorphisms publ math inst hautes etudes sci 50 1979 101 151 it turns out that in the space of c r smooth diffeomorphisms diff r m of a compact surface m there is an open set u such that a baire generic diffeomorphism f u has infinitely many coexisting sinks in this paper we make a step towards understanding how often does a surface diffeomorphism have infinitely many sinks our main result roughly says that with probability one for any positive d a surface diffeomorphism has only finitely many localized sinks either of cyclicity bounded by d or those whose period is relatively large compared to its cyclicity it verifies a particular case of palis conjecture saying that even though diffeomorphisms with infinitely many coexisting sinks are baire generic they have probability zero one of the key points of the proof is an application of newton interpolation polynomials to study the dynamics initiated in v kaloshin b hunt a stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms i ann of math in press 92 pp v kaloshin a stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms ii preprint 85 pp

nonlinear membership functions in multiobjective fuzzy optimization of mechanical and structural systems an application of fuzzy mathematical programming techniques to multiple objective design problems is presented two examples dealing with the multiobjective design of mechanical and structural systems are considered the concept of a pareto optimal and fuzzy pareto optimal solution is discussed and it is shown that the resulting formulation yields pareto optimal solutions the fundamental assumption in fuzzy mathematical programming applications involving the use of linear membership functions is critically examined several nonlinear shapes for the membership functions of the fuzzy sets are proposed consistent with varying perceptions of the designer and are analyzed to determine their impact on the overall design process these shapes correspond to what we define as the coefficient of membership satiation it is seen that optimum designs for both examples are strongly influenced by the sign of the membership satiation coefficient

strange attractors across the boundary of hyperbolic systems we study a bifurcation of axiom a hyperbolic vector fields in dimension three leading to robust strange attractors with singularities the axiom a vector fields involved in the bifurcation exhibit a basic set equivalent to the suspension of a three symbol subshift the attractors arising from this kind of bifurcation are not equivalent to the geometric lorenz attractors

using historical controls in the analysis of developmental toxicity data historical control data can often aid in the interpretation of the results from laboratory dose response experiments for example formal statistical methods for using historical data are well established for carcinogenicity studies in that case a score test derived from a beta binomial model yields a simple modification of the standard cochran armitage test for trend however this test cannot be used for developmental toxicity studies since it does not allow for the additional correlation structure induced by the presence of litter effects in this paper quasi likelihood methods are used to incorporate historical control information into a trend test for the types of correlated binary outcomes that typically arise in developmental toxicity studies the proposed test is asymptotically equivalent to the beta binomial score test in the special case when all the litter sizes are equal to 1 malformation data from a series of developmental toxicity studies illustrate the results

power comparisons for tests of trend in dose response studies the cochran armitage test for trend is a popular statistical procedure for detecting increasing or decreasing probabilities of response when a categorical exposure is ordered such associations may arise in a variety of biomedical research settings particularly in dose response designs such as carcinogenicity experiments previously computing limitations mandated the use of the asymptotic trend test but with the availability of new algorithms increased computing power and appropriate software the exact trend test is now a practical option nevertheless the exact test is sometimes criticized on the grounds that it is conservative in this paper we investigate the implications of this conservatism by comparing the true type i error and power of three alternative tests of trend the asymptotic test the exact test and an admissible exact test proposed by cohen and sackrowitz the computations are performed by an extension to the network algorithm of mehta et al this allows us to make precise power comparisons between the tests under any given design without resorting to simulation we show how this tool can guide investigators in choosing the most appropriate test by considering the design of two year carcinogenicity studies carried out by the national toxicology program we additionally compare the tests for various other combinations of sample sizes and number of groups or levels of exposure we conclude that the asymptotic test while more powerful where it is valid generally does not preserve the type i error this violation of the a priori testing level can be greatly affected by imbalance in the data or unequal spacing of dose levels

suppression of chaos by cyclic parametric excitation in two dimensional maps we study the qualitative change of the dynamics of a generalized two dimensional quadratic map under the influence of parametric perturbations which operate in the chaotic parameter set it is shown that such perturbations can lead to the suppression of chaos and appearance of a regular periodic behaviour numerically we can argue that the suppression of chaos due to the parametric excitation is caused by a shift of the windows of periodic behaviour in the bifurcation diagram

rapid decay of correlations for nonuniformly hyperbolic flows we show that superpolynomial decay of correlations rapid mixing is prevalent for a class of nonuniformly hyperbolic flows these flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which young proved exponential decay of correlations the proof combines techniques of dolgopyat and operator renewal theory it follows from our results that planar periodic lorentz flows with finite horizons and flows near homoclinic tangencies are typically rapid mixing

singular heteroclinic cycles abstract we study the unfolding of heteroclinic cycles of vector fields in r n that possess a hyperbolic singularity and a saddle node the principal eigenvalues at the hyperbolic singularity are assumed to be real but the weak hyperbolic eigenvalues at the saddle node may be either real or complex conjugate we discuss the bifurcation diagrams of all codimension two such bifurcations in some of the occurring cases chaotic dynamics appears in the unfolding for the cases with only simple dynamics in the unfolding we obtain the complete bifurcation diagram we derive exponential expansions for the transition map near the saddle node

at the other side of a saddle node we describe phenomena occurring just before a saddle node bifurcation for one parameter families of interval maps in particular as a parameter approaches the bifurcation value attracting periodic orbits of periodsk k 1 k 2 k 3 can appear we make a detailed study of a family of cusp shaped maps where this phenomenon occurs in a pure form

bifurcation analysis of a system of coupled chemical oscillators bromate chlorite iodine abstract we examine the dynamical behavior of two chemical oscillators bromate iodide and chlorite iodide as well as the coupled system bromate chlorite iodide study of the period and amplitude of oscillation at the bifurcation points yields phase portraits for the uncoupled systems these are combined to give insights into the nature of the higher dimensional coupled system which exhibits a wide variety of dynamical phenomena including multiple stationary states birhythmicity and chaos analysis of the topology of the phase portraits and of the experimentally determined return map suggests that the coupled system may possess a lorenz type attractor

the use of historical control information in testing for a trend in proportions a problem commonly faced in biometric applications is to test for a trend in proportions in a 2 x k contingency table in which the k columns have a natural ordering for example a test compound may be administered at increasing dose levels to groups of test animals to determine if the proportion of animals developing a tumor increases with increasing dose level cochran 1954 and armitage 1955 proposed a chi square statistic for testing for a trend in proportions for problems with a large amount of historical data a test for trend incorporating the historical data would be useful this paper develops such a test based on a statistic which is closely related to that of cochran and armitage this method for binomial proportions is analogous to the method derived by pocock 1976 for normallydistributed data the problem will be developed in the context of an animal carcinogenesis experiment consider an experiment involving r 1 groups of test animals one group serves as a control group and the remaining r groups are given a test compound at increasing dose levels dld2 dr the animals are followed for a fixed period of time and the number of animals which develop a tumor at a particular organ is recorded for each group let ni denote the number of animals in the ith group and let the number of these animals which develop a tumor during the course of the experiment be denoted by xi i 0 1 r the results of this experiment can be summarized in a 2 x r 1 table such as table 1 to test for ap increase in the proportions pi xjni with increasing dose level cochran and armitage suggested the test statistic

on the use of historical control data to estimate dose response trends in quantal bioassay new tests for trend in proportions in the presence of historical control data are proposed one such test is a simple score statistic based on a binomial likelihood for the current study and beta binomial likelihoods for each historical control series a closely related trend statistic based on estimating equations is also proposed trend statistics that allow overdispersed proportions in the current study are also developed including a version of tarone s 1982 biometrics 38 215 220 test that acknowledges sampling variation in the beta distribution parameters and a trend statistic based on estimating equations each such trend test is evaluated with respect to size and power under both binomial and beta binomial sampling conditions for the current study and illustrations are provided

strange attractors and wandering domains near a homoclinic cycle to a bifocus abstract in this paper we explore the three dimensional chaotic set near a homoclinic cycle to a hyperbolic bifocus at which the vector field has negative divergence if the invariant manifolds of the bifocus satisfy a non degeneracy condition a sequence of hyperbolic suspended horseshoes arises near the cycle with one expanding and two contracting directions we extend previous results on the field and we show that the first return map to a given cross section may be approximated by a map exhibiting heteroclinic tangencies associated to two periodic orbits under an additional hypothesis about the coexistence of two heteroclinically related periodic points one without dominated splitting into one dimensional sub bundles the heteroclinic tangencies can be slightly modified in order to satisfy tatjer s conditions for a generalized tangency of codimension two this configuration may be seen as the organizing center by which one can obtain bogdanov takens bifurcations and therefore strange attractors infinitely many sinks and non trivial contracting wandering domains

optimum design of structures in a fuzzy environment the basic concepts of the theory of fuzzy sets and its applications are briefly reviewed a method is then presented for solving fuzzy optimization problems using ordinary nonlinear programming techniques along with a numerical example possible applications of the approach described here are mentioned including application to the analysis of structural failures and development of expert systems for structural design 9 references

solution of the basin problem for henon like attractors for a large class of non uniformly hyperbolic attractors of dissipative diffeomorphisms we prove that there are no holes in the basin of attraction stable manifolds of points in the attractor fill in a full lebesgue measure subset then lebesgue almost every point in the basin is generic for the srb sinai ruelle bowen measure of the attractor this solves a problem posed by sinai and by ruelle for this class of systems

hyperbolicity and the creation of homoclinic orbits we consider one parameter families sp t e r of diffeomorphisms on surfaces which display a homoclinic tangency for yt 0 and are hyperbolic for yt 0 i e pf has a hyperbolic nonwandering set the tangency unfolds into transversal homoclinic orbits for yt positive for many of these families we prove that p is also hyperbolic for most small positive values of yt which implies much regularity of the dynamical structure a main assumption concerns the limit capacities of the basic set corresponding to the homoclinic tangency

fuzzy goal programming approach for structural optimization a fuzzy nonlinear goal programming approach is presented for solving multiobjective optimization problems involving vague and imprecise information several computational models including simple additive weighted additive and preemptive priority models are given for the numerical solution of the problem the methodolo gies are illustrated with the help of two structural optimization problems involving multiple goals the solution of the first example is obtained using a graphical procedure whereas the second example is solved using nonlinear programming techniques linear membership functions are used in the numerical work for simplicity the methodologies presented in this work aid in the preliminary design of structural systems involving imprecise and vague information about the goals and or constraints inear goal programming has been extensively used in solving decision making problems involving linear equa tions and multiple conflicting goals the goals can be rank ordered depending on their importance to the decision maker goal programming attempts to achieve as man 7 of these goals as possible by minimizing deviational variables from the goal levels depending on their relative weights linear goal pro gramming algorithms were developed by charnes et al 1 ig nizio 2 and zanakis and gupta 3 the extension of goal pro gramming to nonlinear optimization problems has also been considered by several authors 3 4 a fuzzy programming ap proach for linear programming problems with several objec tives was suggested by zimmerman 5 subsequently several authors proposed different fuzzy goal programming ap proaches for solving linear goal programming problems in volving imprecise statements and information 6 10 narasimhan6 suggested a method for solving fuzzy linear goal programming problems under the assumption of linear membership functions his method involves solving a set of 2k linear programming problems each containing 3k constraints where k denotes the number of goals in the original problem hannan7 indicated a procedure for formulating a fuzzy goal programming problem as an equivalent single linear program ming problem with 2k goal related constraints the problems associated with the definition of fuzzy priorities were dis cussed in ref 7 a brief review of the history and the state of the art in fuzzy multicriteria programming as of 1982 was presented by ignizio 8 the distinction between fuzzy goal pro gramming and fuzzy multicriteria formulations was given in ref 9 models are presented by hannan7 for the use of fuzzy goal programming with preemptive priorities with archime dian weights and with the maximization of the membership function corresponding to the minimum goal a methodology based on the use of a nested hierarchy of priorities for each goal was presented by rubin and narasimhan 10 the impor tance of multiple objectives in the design of practical engineer

abundance of c 1 robust homoclinic tangencies a diffeomorphism f has a c 1 robust homoclinic tangency if there is a c 1 neighbourhood u of f such that every diffeomorphism in g u has a hyperbolic setg depending contin uously on g such that the stable and unstable manifolds ofg have some non transverse intersection for every manifold of dimension greater than or equal to three we exhibit a lo cal mechanism blender horseshoes generating diffeomorphisms with c 1 robust homoclinic tangencies using blender horseshoes we prove that homoclinic classes of c 1 generic diffeomorphisms containing saddles with different indices and that do not admit dominated splittings of appropriate dimensions display c 1 robust homoclinic tangencies

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

use of historical controls in time adjusted trend tests for carcinogenicity we develop a method for incorporating historical control information into time adjusted tests for dose effects in carcinogenicity studies after discretizing the time scale we use a multinomial distribution to model the number of animals dying with tumor in each interval data from past studies are used to estimate the parameters characterizing the prior a score test derived from the resulting dirichlet multinomial generalizes the test of tarone 1982 biometrics 38 215 220 and reduces in the limit to the log rank test in the case of a diffuse prior the methodology is illustrated with data from a study of the fire retardant 2 2 bis bromomethyl 1 3 propanediol