analytic invariant manifolds for sequences of diffeomorphisms abstract we obtain real analytic invariant manifolds for trajectories of maps assuming only the existence of a nonuniform exponential behavior we also consider the more general case of sequences of maps which corresponds to a nonautonomous dynamics with discrete time we emphasize that the maps that we consider are defined in a real euclidean space and thus one is not able to obtain the invariant manifolds from a corresponding procedure to that in the nonuniform hyperbolicity theory in the context of holomorphic dynamics we establish the existence both of stable and unstable manifolds and of center manifolds as a byproduct of our approach we obtain an exponential control not only for the trajectories on the invariant manifolds but also for all their derivatives

on interval enclosures using slope arithmetic this paper describes how a combination of interval derivative arithmetic and interval slope arithmetic can be used with the programming language pascal sc to obtain an enclosure of the range of a factorable function r n r 1 with c 2 d which is often narrower than that which is obtained by using slope arithmetic alone and which is always narrower than that which is obtained by using interval derivative arithmetic alone

real root classification of parametric spline functions abstract the real root classification of a given parametric spline function is a collection of possible cases of its real root distribution on every interval together with the conditions of its coefficients must be satisfied for each case this paper presents an algorithm to deal with the real root classification of a given parametric spline function two examples are provided to illustrate the proposed algorithm is flexible

statistical properties of chaotic systems the theory of smooth dynamical systems and the theory of abstract dynamical systems ergodic theory although having the same roots have for many years developed quite independently of one another these theories have now matured to the point where they can be combined to shed light on the nature of chaotic behavior

equidistribution of saddle periodic points for henon type automorphisms of mathbb c k in this paper we prove the equidistribution of saddle periodic points for henon type automorphisms of mathbb c k with respect to its equilibrium measure a general strategy to obtain equidistribution properties in any dimension is presented it is based on our recent theory of densities for positive closed currents several fine properties of dynamical currents are also proved

an unconditionally convergent method for computing zeros of splines and polynomials we present a simple and ecient method for computing zeros of spline functions the method exploits the close relationship between a spline and its control polygon and is based on repeated knot insertion like newton s method it is quadratically convergent but the new method overcomes the principal problem with newton s method in that it always converges and no starting value needs to be supplied by the user

complexities of differentiable dynamical systems we define the notion of localizable property for a dynamical system then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems these notions are the fast growth of the number of periodic points the positive entropy and the high emergence we finally propose a dictionary between the previously explained theory on entropy and the ongoing one on emergence

green currents for holomorphic automorphisms of compact kahler manifolds and some additional regularity properties very likely the currents t will describe the distribution of invariant manifolds of codimension s corresponding to the small est lyapounov exponents let dp denote the dynamical degree of order p of it describes the growth under iteration of the volume of p dimensional manifolds when d 1 it is natural to introduce first a positive closed 1 l current as ifnyoj 7 lim

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

sur les groupes de transformations birationnelles des surfaces ni agissant par transformations bi rationnelles sur les surfaces complexes compactes kahl eriennes nous mon trons a que le groupe des transformations birationnelles d une surface satisfait l alternative de tits b que les actions birationnelles de groupes de kazhdan sur les surfaces sont toutes birationnellement conjugu eesa des actions homographiques sur le plan projectif et c que si f et g sont deux transformations birationnelles de surfaces qui commutent alors ou bien f pr eserve un pinceau de courbes ou bien l un des it er es g m de g m 0 concide avec un it er e f n de f n 2 z let s be any compact complex kahler surface and bir s the group of birational transformations of s we study the structure of nitely genera ted subgroups of bir s and prove three main results a bir s satises the tits alternative b if a group with kazhdan property t acts on a compact kahler surface by birational transformations then the action is conjugate to an action by linear projective transformations on the projec tive plane and c if f is an element of bir s which does not preserve any pencil of curves and if g commutes with f then a positive iterate of g coincides with an iterate of f the second statement provides a positive answer to zimmer s conjecture for birational actions on surfaces

subdivision algorithms converge quadratically this paper is concerned with determining the exact convergence rates of subdivision algorithms for various settings of polynomial and spline curve or surface representations

near minimally normed spline quasi interpolants on uniform partitions spline quasi interpolants qis are local approximating operators for functions or discrete data we consider the construction of discrete and integral spline qis on uniform partitions of the real line having small infinity norms we call them near minimally normed qis they are exact on polynomial spaces and minimize a simple upper bound of their infinity norms we give precise results for cubic and quintic qis also the qi error is considered as well as the advantage that these qis present when approximating functions with isolated discontinuities

technical communique on stability of second order quasi polynomials with a single delay in this note the stability of a second order quasi polynomial with a single delay is studied although there is a vast literature on this problem most available solutions are limited to some particular cases moreover some published results on this subject appear to contain imprecise or even wrong conditions the purpose of this note is to show that by accurate application of known theories a complete explicit characterization of stability regions can be derived in a most general case as a byproduct of the proposed analysis we show that in the high order case the quasi polynomial is delay independent unstable whenever its delay free version has an odd number of unstable roots or equivalently a negative static gain

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

solving parametric piecewise polynomial systems we deal with c r smooth continuity conditions for piecewise polynomial functions on d where d is an algebraic hypersurface partition of a domain w in r n piecewise polynomial functions of degree at most k on d that are continuously differentiable of order r form a spline space c k r we present a method for solving parametric systems of piecewise polynomial equations of the form z f 1 f n email protected email protected f 1 v x 0 f n v x 0 where f email protected c k w r w d and f w s email protected q v x for each n cell s i in d v u 1 u 2 u t is the set of parameters and x x 1 x 2 x n is the set of variables s 1 s 2 s m are all the n dimensional cells in d and email protected i 1 email protected i based on the discriminant variety method presented by lazard and rouillier we show that solving a parametric piecewise polynomial system z f 1 f n is reduced to the computation of discriminant variety of z the variety can then be used to solve the parametric piecewise polynomial system we also propose a general method to classify the parameters of z f 1 f n this method allows us to say that if there exist an open set of the parameters space where the system admits exactly a given number of distinct torsion free real zeros in every n cells in d

a bibliography on roots of polynomials abstract a categorized bibliography on roots of polynomials is presented covering the period from the earliest times until late 1990 the actual bibliography is on a computer diskette accompanying this issue together with programs designed to print parts of the main work such as entries belonging to a certain category

polynomial diffeomorphisms of c 2 viii quasi expansion we introduce the notion of quasi expansion in the context of polynomial diffeomorphisms of c 2 like hyperbolic diffeomorphisms quasi expanding maps have uniformly large multipliers at saddle points on the other hand unlike the hyperbolic case quasi expanding maps can have tangencies between stable and unstable manifolds we characterize quasi expansion in a number of ways and develop some of the structure they possess quasi expansion was motivated by the study of real polynomial diffeomorphisms of maximal entropy and our study of maximal entropy diffeomorphisms relies on the results of this paper

polynomial diffeomorphisms of ii stable manifolds and recurrence f x y y y ax c the diffeomorphisms in this class have complicated dynamics in particular they have periodic points of infinitely many periods and positive topological entropy see fm s we can distinguish between these classes by considering the growth of the degrees of iterates of the diffeomorphism define deg f to be the maximum of the degrees of the coordinate functions this quantity is not a conjugacy invariant of f hence not a dynamical invariant we can construct a conjugacy invariant which we call the dynamical degree as follows

computing the range of values of real functions using b spline form abstract in this paper we present an easy and efficient method for computing the range of a function by using spline quasi interpolation we exploit the close relationship between the spline function and its control polygon and use tight subdivision technique in order to obtain monotonic splines which make the range of the spline easy to compute the proposed method is useful in case of given scattered data generated by some unknown function f or scientific measurements several numerical examples are given for cubic and quintic quasi interpolant approximant to illustrate the efficiency and the performance of our method

an algorithm for multi resolution analysis of nurbs surfaces a new algorithm is proposed for the multi resolution representation of nurbs non uniform rational b spline surfaces with boundary consistency constraints the kernel idea is to employ t meshes t spline control meshes to construct the multi resolution representation for surfaces to this end the original b mesh b spline control mesh is first divided into a boundary part and an inner one then the multi resolution representation of the inner part is achieved by wavelet transform at last the topology of the boundary part is added onto the obtained multi resolution meshes to construct the final t spline based multi resolution representation result the boundary shapes keep unchanged in the whole process of the treatment because the boundary consistency constraints are always contained in the boundary part this advantage of the new algorithm is demonstrated by three examples

on compactly supported spline wavelets and a duality principle let v 1 v 0 v 1 be a multiresolution analysis of l 2 generated by the mth order b spline n m x we exhibit a compactly supported basic wavelet m x that generates the corresponding orthogonal complementary wavelet subspaces w 1 w 0 w 1 consequently the two finite sequences that describe the two scale relations of n m x and m x in terms of n m 2x j j z yield an efficient reconstruction algorithm to give an efficient wavelet decomposition algorithm based on these two finite sequences we derive a duality principle which also happens to yield the dual bases n m x j and 59 m x j relative to n m x j and m x j respectively

feedback stabilization of a 1 d linear reaction diffusion equation with delay boundary control the goal of this paper is to design a stabilizing feedback boundary control for a reaction diffusion partial differential equation pde where the boundary control is subject to a constant delay while the equation may be unstable without any control for this system which is equivalent to a parabolic equation coupled with a transport equation a prediction based control is explicitly computed by splitting the infinite dimensional system into two parts a finite dimensional unstable part and a stable infinite dimensional part a finite dimensional delayed controller is computed for the unstable part and it is shown that this controller stabilizes the whole pde the proof is based on an explicit expression of the classical artstein transformation combined with an adequately designed lyapunov function a numerical simulation illustrates the constructive feedback design method

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

computing slope enclosures by exploiting a unique point of inflection using slope enclosures may provide sharper bounds for the range of a function than using enclosures of the derivative hence slope enclosures may be useful in verifying the assumptions for existence tests or in algorithms for global optimization previous papers by kolev and ratz show how to compute slope enclosures for convex and concave functions in this paper we generalize these formulas and show how to obtain slope enclosures for a function that has exactly one point of inflection or whose derivative has exactly one point of inflection

dynamics of horizontal like maps in higher dimension we study the regularity of the green currents and of the equilibrium measure associated to a horizontal like map in under a natural assumption on the dynamical degrees we estimate the speed of convergence towards the green currents the decay of correlations for the equilibrium measure and the lyapounov exponents we show in particular that the equilibrium measure is hyperbolic we also show that the green currents are the unique invariant vertical and horizontal positive closed currents the results apply in particular to henon like maps to regular polynomial automorphisms of and to their small perturbations

on the optimal stability of the bernstein basis we show that the bernstein polynomial basis on a given interval is optimally stable in the sense that no other nonnegative basis yields systematically smaller condition numbers for the values or roots of arbitrary polynomials on that interval this result follows from a partial ordering of the set of all nonnegative bases that is induced by nonnegative basis transformations we further show by means of some low degree examples that the bernstein form is not uniquely optimal in this respect however it is the only optimally stable basis whose elements have no roots on the interior of the chosen interval these ideas are illustrated by comparing the stability properties of the power bernstein and generalized ball bases

well posedness of boundary control systems continuity of the input output map for boundary control systems is shown through the system transfer function our approach transforms the question of continuity of the input output map of a boundary control system to uniform boundedness of the solution to a related elliptic problem this is shown for a class of boundary control systems with dirichlet neumann or robin boundary control

parametric robust structured control design we present a new approach to parametric robust controller design where we compute controllers of arbitrary order and structure which minimize the worst case h infty norm over a pre specified set of uncertain parameters at the core of our method is a nonsmooth minimization method tailored to functions which are semi infinite minima of smooth functions a rich test bench and a more detailed example illustrate the potential of the technique which can deal with complex problems involving multiple possibly repeated uncertain parameters

fine topology silov boundary and ddc n on considere la topologie fine des fonctions plurisousharmoniques on etablit des theoremes de convergence on etudie les definitions de dd c n l operateur dd c n converge pour des limites monotones des fonctions plurisousharmoniques bornees

dynamics of regular polynomial endomorphisms of c k a regular polynomial self mapping of complex euclidean space has a continuous extension to the hyperplane at infinity the induced mapping at infinity is used to describe the dynamics of the self mapping in a neighborhood of infinity a theory of external rays is developed to provide the connection between the behavior at infinity and the behavior on the finite plane

the julia set of henon maps in this paper we investigate the support of the unique measure of maximal entropy of complex henon maps j the main question is whether this set is the same as the analogue of the julia set j

stability and bifurcations for dissipative polynomial automorphisms of mathbb c 2 we study stability and bifurcations in holomorphic families of polynomial automorphisms of mathbb c 2 we say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there we first show that this defines a meaningful notion of stability which parallels in many ways the classical notion of j stability in one dimensional dynamics define the bifurcation locus to be the complement of the weak stability locus in the second part of the paper we prove that under an assumption of moderate dissipativity the parameters displaying homoclinic tangencies are dense in the bifurcation locus this confirms one of palis conjectures in the complex setting the proof relies on the formalism of semi parabolic bifurcation and the construction of critical points in semi parabolic basins which makes use of the classical denjoy carleman ahlfors and wiman theorems

a new pruning test for finding all global minimizers of nonsmooth functions a new pruning test is presented via interval slopes for finding all global minimizers of nonsmooth functions of several variables based on an expansion scheme which can be used to achieve better interval slopes and enclosure of function ranges the presented pruning test extends ratz s a nonsmooth global optimization technique using slopes one dimensional case j global optimiz 4 1999 365 393 pruning technique which can be extensively applied in several variable nonsmooth global optimization as a accelerating device this new pruning test is similar to the monotonicity test frequently used in interval methods for smooth problems but it improves the monotonicity test numerical results show that the proposed global optimization algorithm with the new pruning test is better than that with the monotonicity test for smooth functions and superior to other interval algorithm for nonsmooth functions

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

a new multi section based technique for constrained optimization problems with interval valued objective function in this paper an efficient optimization technique is proposed for constrained optimization problems with interval valued objective function at first the significance of interval valued objective function and the meaning of the interval valued solution of the proposed problem have been explained with graphical interpretation generally this type of problems has infinitely many compromise solutions the aim of this approach is to obtain one of such solutions with higher accuracy and lower computational cost the proposed technique is mainly based on the splitting criterion of the accepted prescribed search region calculation of the interval inclusion functions and the selection of subregion depending on the modified interval order relations in the context of the decision makers point of view novel interval oriented constraint satisfaction rules are used for non interval equality and inequality constraints clearly the proposed technique is nothing but an imitation of well known interval analysis based branch and bound b b optimization approach the modified multi section division criterion with some new interval oriented constraint satisfaction rules for non interval valued equality and inequality constraints and some novel interval order relations in the context of the decision makers point of view have been applied to increase the efficiency of the proposed algorithm finally the technique is applied for solving some test problems and the results are compared with the same obtained from the existing methods

a multiresolution analysis for tensor product splines using weighted spline wavelets we construct biorthogonal spline wavelets for periodic splines which extend the notion of lazy wavelets for linear functions where the wavelets are simply a subset of the scaling functions to splines of higher degree we then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight function using the lifted wavelets we define a multiresolution analysis of tensor product spline functions and apply it to image compression of black and white images by performing as a model problem image compression with black and white images we demonstrate that the use of a weight function allows to adapt the norm to the specific problem

rational cubic clipping with linear complexity for computing roots of polynomials many problems in computer aided geometric design and computer graphics can be turned into a root finding problem of polynomial equations among various clipping methods the ones based on the bernstein bezier form have good numerical stability one of such clipping methods is the k clipping method where k 2 3 and often called a cubic clipping method when k 3 it utilizes o n2 time to find two polynomials of degree k bounding the given polynomial f t of degree n and achieves a convergence rate of k 1 for a single root the roots of the bounding polynomials of degree k are then used for bounding the roots of f t this paper presents a rational cubic clipping method for finding two bounding cubics within o n time which can achieve a higher convergence rate 5 than that of 4 of the previous cubic clipping method when the bounding cubics are obtained the remaining operations are the same as those of previous cubic clipping method numerical examples show the efficiency and the convergence rate of the new method

the maximum number and its distribution of singular points for parametric piecewise algebraic curves abstract the piecewise algebraic curve as the zero set of a bivariate spline function is a generalization of the classical algebraic curve based on the previous method presented by lai et al 2009 we show that computing singular points of parametric piecewise algebraic curves amounts to solving parametric piecewise polynomial systems in this article we give a method to compute the maximum number and its distribution of singular points for a given parametric piecewise algebraic curve this method also produces necessary and sufficient conditions of its parameters must be satisfied an illustrated example shows that our method is flexible

justification of input output methods for systems with unbounded control and observation the authors present definitions of feedback stabilizability and detectability that are weaker than those previously appearing in the literature stabilizability and detectability in this sense are sufficient to ensure an equivalence between internal and external stability for well posed systems furthermore stabilizability and detectability are shown to be preserved under feedback and other connections these results are linked to present a justification of input output controller design methods for systems with unbounded control and observation

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

un phenomene de concentration de genre we show that the main part of the genus of the preimages of a projective line by a generic holomorphic endomorphism of goes to the support of the green measure

dynamics of automorphisms on compact kahler manifolds we study holomorphic automorphisms on compact kahler manifolds having simple actions on the hodge cohomology ring we show for such automorphisms that the main dynamical green currents admit complex laminar structures woven currents and the green measure is the unique invariant probability measure of maximal entropy

interval approximation of higher order to the ranges of functions the bernstein and b spline forms are generalized to multivariate polynomials these forms are combined with a type of taylor form for multivariate functions to generate realizable forms for multivariate functions

stable manifolds for holomorphic automorphisms we give a sucient condition for the abstract basin of attraction of a sequence of holomorphic self maps of balls in c d to be biholomorphic to c d as a consequence we get a sucient condition for the stable manifold of a point in a compact hyperbolic invariant subset of a complex manifold to be biholomorphic to a complex euclidean space our result immediately implies previous theorems obtained by jonsson varolin and by peters in particular we prove without using oseledec s theory that the stable manifold of any point where the negative lyapunov exponents are well dened is biholomorphic to a complex euclidean space our approach is based on the solution of a linear control problem in spaces of subexponential sequences and on careful estimates of the norm of the conjugacy operator by a lower triangular matrix on the space of k homogeneous polynomial endomorphisms of c d mathematics subject classication 2010 primary 37f99 secondary 32h50 37d25 37h99

the dimension of the maximal measure for a polynomial map let f c c be a polynomial of degree d 2 the most interesting dynamics of f takes place on its julia set j f an invariant compact perfect set which can be defined for example as the closure of the repelling periodic points brolin constructed the equilibrium distribution m on j f an ergodic measure which is also the weak limit as n x of a probability measure distributed equally over the dn nth inverse images of almost any point we shall prove the following

output feedback adaptive control of a wave pde with boundary anti damping abstract we develop an adaptive output feedback controller for a wave pde in one dimension with actuation on one boundary and with an unknown anti damping term on the opposite boundary this model is representative of a torsional stick slip instability in drillstrings in deep oil drilling as well as of various acoustic instabilities the key feature of the proposed controller is that it requires only the measurements of boundary values and not of the entire distributed state of the system our approach is based on employing riemann variables to convert the wave pde into a cascade of two delay elements with the first of the two delay elements being fed by control and the same element in turn feeding into a scalar ode this enables us to employ a prediction based design for systems with input delays suitably converted to the adaptive output feedback setting the result s relevance is illustrated with simulation example

the metric entropy of diffeomorphisms soit m une variete de riemann compacte c sans bord soit f un diffeomorphisme c 2 de m et soit m une mesure de probabilite de borel f invariante sur m soit h m f l entropie de f on donne des relations entre h m f et les proprietes geometriques de f et de m

continuity properties of entropy on donne une borne superieure sur le defaut en semicontinuite superieure des entropies topologiques et metriques d une auto application c r d une variete c r r 1

semi parabolic bifurcations in complex dimension two parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena in this paper we consider the bifurcations of a holomorphic diffeomorphism in two complex dimensions with a semi parabolic semiattracting fixed point

dynamics of regular birational maps in p k abstract we develop the study of some spaces of currents of bidegree p p as an application we construct the equilibrium measure for a large class of birational maps of p k as intersection of green currents we show that these currents are extremal and that the corresponding measure is mixing

boundary control of partial differential equations using frequency domain optimization techniques abstract we present a frequency domain based h control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation where controllers are constrained to be physically implementable and of simple structure suited for practical applications the efficiency of our technique is demonstrated by controlling a reaction diffusion equation with input delay and a wave equation with boundary anti damping

a non laminar dynamical green current a holomorphic endomorphism f of mathbb cp 2 admits a julia set j 1 defined as usual to be the locus of non normality of its iterates f n n ge 0 and a typically smaller julia set j 2 which is essentially the closure of the set of repelling periodic orbits the question has been raised whether j 1 setminus j 2 is filled possibly in a measure theoretic sense with fatou subvarieties along which the dynamics is locally equicontinuous in this article we construct examples showing that this is not the case in general

perturbed basins of attraction let f be an automorphism of open image in new window which has an attracting fixed point it is well known that the basin of attraction is biholomorphically equivalent to open image in new window we will show that the basin of attraction of a sequence of automorphisms f 1 f 2 is also biholomorphic to open image in new window if every f n is a small perturbation of the original map f

a structure theorem for semi parabolic henon maps abstract consider the parameter space p c 2 of complex henon maps h c a x y x 2 c a y a x a 0 which have a semi parabolic fixed point with one eigenvalue e 2 i p q in this paper we provide a complete topological description of the julia set and forward julia set within a family of semi parabolic henon maps i e those henon maps from the curve p which are perturbations of a quadratic polynomial p with a parabolic fixed point of multiplier we prove that there is an open disk of parameters in p for which the semi parabolic henon map has connected julia set j and is structurally stable on j and j the forward julia set j has a nice local description inside a certain bidisk it is a trivial fiber bundle over j p the julia set of the polynomial p with fibers biholomorphic to a disk the julia set j is homeomorphic to the quotient of a solenoid by an equivalence relation and j j the closure of the saddle periodic points

an improved rational cubic clipping method for computing real roots of a polynomial abstract the root finding problem has wide applications in geometric processing and computer graphics previous rational cubic clipping methods are either of convergence rate 7 k with o n2 complexity or of convergence rate 5 k with linear complexity where n and k are degree of the given polynomial and the multiplicity of the root respectively this paper presents an improved rational cubic clipping of linear complexity which can achieve convergence rate 7 k or a better one 7 k 1 for a multiple root such that k 2 numerical examples illustrate both efficiency and convergence rate of the new method

methods for bounding the range of a polynomial a class of methods for computing including estimates for the range of a polynomial over an interval is defined the two special cases of the bernstein form and the b spline form are shown to be members of the class

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

boundary control of an anti stable wave equation with anti damping on the uncontrolled boundary abstract much of the boundary control of wave equations in one dimension is based on a single principle passivity under the assumption that control is applied through neumann actuation on one boundary and the other boundary satisfies a homogeneous dirichlet boundary condition we have recently expanded the scope of tractable problems by allowing destabilizing anti stiffness a robin type condition on the uncontrolled boundary where the uncontrolled system has a finite number of positive real eigenvalues in this paper we go further and develop a methodology for the case where the uncontrolled boundary condition has anti damping which makes the real parts of all the eigenvalues of the uncontrolled system positive and arbitrarily high i e the system is anti stable exponentially stable in negative time using a conceptually novel integral transformation we obtain extremely simple explicit formulae for the gain functions for the case with only boundary sensing available at the same end with actuation we design backstepping observers which are dual to the backstepping controllers and have explicit output injection gains we then combine the control and observer designs into an output feedback compensator and prove the exponential stability of the closed loop system

attracting currents and equilibrium measures for quasi attractors of mathbb p k let f be a holomorphic endomorphism of mathbb p k of degree d for each quasi attractor of f we construct a finite set of currents with attractive behaviors to every such attracting current is associated an equilibrium measure which allows for a systematic ergodic theoretical approach in the study of quasi attractors of mathbb p k as a consequence we deduce that there exist at most countably many quasi attractors each one with topological entropy equal to a multiple of log d we also show that the study of these analytic objects can initiate a bifurcation theory for attracting sets

nonsmooth h_infty synthesis we develop nonsmooth optimization techniques to solve h infty synthesis problems under additional structural constraints on the controller our approach avoids the use of lyapunov variables and therefore leads to moderate size optimization programs even for very large systems the proposed framework is versatile and can accommodate a number of challenging design problems including static fixed order fixed structure decentralized control design of pid controllers and simultaneous design and stabilization problems our algorithmic strategy uses generalized gradients and bundling techniques suited for the h infty norm and other nonsmooth performance criteria we compute descent directions by solving quadratic programs and generate steps via line search convergence to a critical point from an arbitrary starting point is proved and numerical tests are included to validate our methods the proposed approach proves to be efficient even for systems with several hundreds of states

local quasi interpolants based on special multivariate quadratic spline space over a refined quadrangulation in this paper we describe the construction of a suitable normalized b spline representation for special multivariate quadratic spline space s 2 1 0 d over a refined quadrangulation we then develop as an application a general theory of quasi interpolants based on this representation

real topological entropy versus metric entropy for birational measure preserving transformations abstract we consider a family of birational measure preserving transformations of two complex variables depending on one parameter for which simple rational expressions for the dynamical zeta function have been conjectured together with an equality between the topological entropy and the logarithm of the arnold complexity divided by the number of iterations similar results have been obtained for the adaptation of these two concepts to dynamical systems of real variables yielding to introduce a real topological entropy and a real arnold complexity we try to compare here the kolmogorov sinai metric entropy and this real arnold complexity or real topological entropy on this particular example of a one parameter dependent birational transformation of two variables more precisely we analyze using an infinite precision calculation the lyapunov characteristic exponents for various values of the parameter of the birational transformation in order to compare these results with the ones for the real arnold complexity we find a quite surprising result for this very birational example and in fact for a large set of birational measure preserving mappings generated by involutions the lyapunov characteristic exponents seem to be equal to zero or at least extremely small for all the orbits we have considered and for all values of the parameter birational measure preserving transformations generated by involutions could thus allow to better understand the difference between the topological description and the probabilistic description of discrete dynamical systems many birational measure preserving transformations generated by involutions seem to provide examples of discrete dynamical systems which can be topologically chaotic while they are metrically almost quasi periodic heuristically this can be understood as a consequence of the fact that their orbits seem to form some kind of transcendental foliation of the two dimensional space of variables

loewner equations on complete hyperbolic domains abstract we prove that on a complete hyperbolic domain d c q any loewner pde associated with a herglotz vector field of the form h z t z o z 2 where the eigenvalues of have strictly negative real part admits a solution given by a family of univalent mappings f t d c q which satisfies t 0 f t d c q if no real resonance occurs among the eigenvalues of then the family e t f t is uniformly bounded in a neighborhood of the origin we also give a generalization of pommerenke s univalence criterion on complete hyperbolic domains