on the observability of continuous time switched linear systems under partially unknown inputs this technical note addresses the problem of observability of continuous time switched linear systems sls subject to unknown disturbances unknown switching signals and unconstrained nonzero dwell time for this class of hybrid systems a geometric characterization of the observability properties is presented in particular attention is focused on the estimation of the sls state from the continuous measurements using the well known concept of a b invariant subspaces three main problems are addressed and solved namely the observability for every nonzero state trajectory the observability for almost every control input and the observability for almost every state trajectory it is also shown that the approach herein presented subsumes some of the classical results on observability of sls previously reported in the literature and allows expressing them in a common framework

quasi sectorial contractions we revise the notion of the quasi sectorial contractions our main theorem establishes a relation between semigroups of quasi sectorial contractions and a class of m sectorial generators we discuss a relevance of this kind of contractions to the theory of operator norm approximations of strongly continuous semigroups

the norm convergence of the trotter kato product formula with error bound the norm convergence of the trotter kato product formula with error bound is shown for the semigroup generated by that operator sum of two nonnegative selfadjoint operators a and b which is selfadjoint

estimate of the difference between the kac operator and the schrodinger semigroup an operator norm estimate of the difference between the kac operator and the schrodinger semigroup is proved and used to give a variant of the trotter product formula for schrodinger operators in thelp operator norm this extends helffer s result in thel2 operator norm to the case in thelp operator norm for more general scalar potentials and with vector potentials the method of the proof is probabilistic based on the feynman kac and feynman kac ito formula

analysis of operator splitting in the nonasymptotic regime for nonlinear reaction diffusion equations application to the dynamics of premixed flames in this paper we mathematically characterize through a lie formalism the local errors induced by operator splitting when solving nonlinear reaction diffusion equations especially in the nonasymptotic regime the nonasymptotic regime is often attained in practice when the splitting time step is much larger than some of the scales associated with either source terms or the diffusion operator when large gradients are present in a series of previous works a reduction of the asymptotic orders for a range of large splitting time steps related to very short time scales in the nonlinear source term has been studied as well as that associated with large gradients but for linearized equations this study provides a key theoretical step forward since it characterizes the numerical behavior of splitting errors within a more general nonlinear framework for which new error estimates can be derived by coupling lie formalism and regularizing effects of the heat equation the validity of these theoretical results is t

some remarks on operator norm convergence of the trotter product formula on banach spaces abstract we extend the trotter kato chernoff theory of strong approximation of c 0 semigroups on banach spaces to operator norm approximation of analytic semigroups with error estimate as application we obtain a criterion for the operator norm convergence of the trotter product formula on banach spaces with error estimate n 1 log n provided one of the generators has a bounded h functional calculus for both results we present versions for approximation in operator ideal norms such as the trace norm or the hilbert schmidt norm finally we give some remarks on the operator norm convergence of the trotter product formula for semigroups acting on a scale of l p spaces

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

prevalence an addendum to prevalence a translation invariant almost every on infinite dimensional spaces bull amer math soc n s 27 1992 no 2 217 238 mr1161274 93k 28018

transformation de fourier et temps d occupation browniens in this paper we study oscillatory stochastic integrals of the form gamma lambda int limits 0 infty exp i lambda b s g s d s where is a non zero parameter andg a square integrable function we study integrability properties of and its behavior as a function of using stochastic calculus techniques martingale theory representation of ito for a random variable of the wiener space lemma of garsia rodemich rumsey we also obtain limit theorems in law related to the variables based upon an asymptotic version of a theorem of knight on orthogonal continuous martingales

zero one laws for the excursions and range of a levy process a 01 law for the excursions of a levy process x from 0 is established and is used to prove that the closed range of x is either a nowhere dense set or else contains an interval including x0

pattern formation in a nonlinear model for animal coats abstract several models have been proposed for describing the formation of animal coat patterns we consider reaction diffusion models due to murray which rely on a turing instability for the pattern selection in this paper we describe the early stages of the pattern formation process for large domain sizes this includes the selection mechanism and the geometry of the patterns generated by the nonlinear system on one two and three dimensional base domains these results are obtained by an adaptation of results explaining the occurrence of spinodal decomposition in materials science as modeled by the cahn hilliard equation we use techniques of dynamical systems viewing solutions of the reaction diffusion model in terms of nonlinear semiflows our results are applicable to any parabolic system exhibiting a turing instability

on the testability of identification in some nonparametric models with endogeneity this paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity the first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions these conditions are typically referred to as completeness conditions the second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions for each of these hypothesis testing problems we provide conditions under which any test will have power no greater than size against any alternative in this sense we conclude that no nontrivial tests for these hypothesis testing problems exist publication abstract

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

structure from motion causally integrated over time we describe an algorithm for reconstructing three dimensional structure and motion causally in real time from monocular sequences of images we prove that the algorithm is minimal and stable in the sense that the estimation error remains bounded with probability one throughout a sequence of arbitrary length we discuss a scheme for handling occlusions point features appearing and disappearing and drift in the scale factor these issues are crucial for the algorithm to operate in real time on real scenes we describe in detail the implementation of the algorithm which runs on a personal computer and has been made available to the community we report the performance of our implementation on a few representative long sequences of real and synthetic images the algorithm which has been tested extensively over the course of the past few years exhibits honest performance when the scene contains at least 20 40 points with high contrast when the relative motion is slow compared to the sampling frequency of the frame grabber 30 hz and the lens aperture is large enough typically more than 30 spl deg of visual field

trotter kato product formula and operator norm convergence we find necessary and sufficient conditions for the operator norm convergence of the trotter kato product formula using them we prove that this convergence takes place i if the resolvent of one of the involved operators is compact either ii if one operator is relatively compact with respect to another one or iii if the product of resolvents of the involved operators is compact

operator splitting for non autonomous evolution equations abstract we establish general product formulas for the solutions of non autonomous abstract cauchy problems the main technical tools are evolution semigroups allowing the direct application of existing results on autonomous problems the results obtained are illustrated by the example of an autonomous diffusion equation perturbed with time dependent potential we also prove convergence rates for the sequential splitting applied to this problem

note on the paper the norm convergence of the trotter kato product formula with error bound by ichinose and tamura the norm convergence of the trotter kato product formula is established with ultimate optimal error bound for the selfadjoint semigroup generated by the operator sum of two selfadjoint operators a generalization is also given to the operator sum of several selfadjoint operators

the local structure of the sample paths of asymmetric cauchy processes precise information about the local evolution of the sample path is obtained using asymptotic estimates for the potential kernel for the capacity of small intervals and unions of intervals and for the hitting distribution of such sets a new construction of local time is obtained and it is shown that except for the completely asymmetric case the range of the process on a line is a nowhere dense set of positive lebesgue measure

notes on the chernoff product formula abstract we revise the strong convergent chernoff product formula and extend it in a hilbert space to convergence in the operator norm topology main results deal with the self adjoint chernoff product formula the non self adjoint case concerns the quasi sectorial contractions

random fourier series and continuous additive functionals of levy processes on the torus let x be an exponentially killed levy process on t n the n dimensional torus that satisfies a sector condition this includes symmetric levy processes let f e denote the extended dirichlet space of x let h f e and let h y y tn denote the set of translates of h that is h y h y we consider the family of zero energy continuous additive functions n t hy y t t n x r as defined by fukushima for a very large class of random functions h we show that j p t n log n p t n 1 2 d is a necessary and sufficient condition for the family n t h y y t t n x r to have a continuous version almost surely here n p t n is the minimum number of balls of radius e in the metric that covers t n where the metric is the energy metric we argue that this condition is the natural extension of the necessary and sufficient condition for continuity of local times of levy processes of barlow and hawkes results on the bounded variation and p variation in t of n t hy for y fixed are also obtained for a large class of random functions h

trotter kato product formula and symmetrically normed ideals abstract it is proven that the trotter product formula converges in the norm of a symmetrically normed ideal of compact operators away from t0 0 if the kac operator the transfer matrix f t e tb 2e tae tb 2 belongs to this ideal for t t0 the result is generalized to the trotter kato product formula moreover if the perturbation b is small relative to a then error bounds for convergence are obtained the results apply to the dixmier trace

observing lyapunov exponents of infinite dimensional dynamical systems can lyapunov exponents of infinite dimensional dynamical systems be observed by projecting the dynamics into n using a typical nonlinear projection map we answer this question affirmatively by developing embedding theorems for compact invariant sets associated with c1 maps on hilbert spaces examples of such discrete time dynamical systems include time t maps and poincare return maps generated by the solution semigroups of evolution partial differential equations we make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite dimensional dynamical system in so doing we adopt an empirical approach and formulate checkable conditions under which a lyapunov exponent computed from experimental data will be a lyapunov exponent of the infinite dimensional dynamical system under study provided the nonlinear projection map producing the data is typical in the sense of prevalence

amenability free subgroups and haar null sets in non locally compact groups the paper has two objectives on the one hand we study left haar null sets a measure theoretic notion of smallness on polish not necessarily locally compact groups on the other hand we introduce and investigate two classes of polish groups which are closely related to this notion and to amenability we show that left haar null sets form a sigma ideal and have the steinhaus property on polish groups which are amenable at the identity and that they lose these two properties in the presence of appropriately embedded free subgroups as an application we prove an automatic continuity result for universally measurable homomorphisms from inverse limits of sequences of amenable locally compact second countable groups to second countable groups

generalizations of srb measures to nonautonomous random and infinite dimensional systems we review some developments that are direct outgrowths of or closely related to the idea of srb measures as introduced by sinai ruelle and bowen in the 1970s these new directions of research include the emergence of strange attractors in periodically forced dynamical systems random attractors in systems defined by stochastic differential equations srb measures for infinite dimensional systems including those defined by large classes of dissipative pdes quasi static distributions for slowly varying time dependent systems and surviving distributions in leaky dynamical systems

dimension splitting for evolution equations in this paper we are concerned with splitting methods for the time integration of abstract evolution equations we introduce an analytic framework which allows us to prove optimal convergence orders for various splitting methods including the lie and peaceman rachford splittings our setting is applicable for a wide variety of linear equations and their dimension splittings in particular we analyze parabolic problems with dirichlet boundary conditions as well as degenerate equations on bounded domains we further illustrate our theoretical results with a set of numerical experiments

detection of symmetry of attractors from observations i theory abstract barany et al 1993 proposed a method for determining the symmetries of attractors of equivariant systems by averaging certain classes of equivariant maps we use an idea in barany et al to re cast definitions of symmetry detectives assuming that we only have access to equivariant observations from the system detecting from observations allows one to perform averaging in spaces that may have much lower dimension than the phase space this paper generalises and develops their suggestion among the generalisations we consider is the use of nonpolynomial detectives and we show using the notion of prevalence of hunt et al 1992 that our detectives and the detectives of barany et al 1993 dellnitz et al 1994 and golubitsky and nicol 1995 give the correct symmetry of attractors almost certainly in a measure theoretic sense we show that detectives can persistently give incorrect symmetries at isolated points in parametrised systems and discuss how to overcome this we show how one can find the symmetry of an attractor from examination of a poincare section in part ii of this article ashwin and tomes apply these results to find symmetries of attractors in a physical system of four coupled electronic oscillators with s4 symmetry

a local time correspondence for stochastic partial differential equations it is frequently the case that a white noise driven parabolic and or hyperbolic stochastic partial differential equation spde can have random field solutions only in spatial dimension one here we show that in many cases where the spatial operator is the l generator of a levy process x a linear spde has a random field solution if and only if the symmetrization of x possesses local times this result gives a probabilistic reason for the lack of existence of random field solutions in dimensions strictly bigger than one in addition we prove that the solution to the spde is holder continuous in its spatial variable if and only if the said local time is holder continuous in its spatial variable we also produce examples where the random field solution exists but is almost surely unbounded in every open subset of space time our results are based on first establishing a quasi isometry between the linear l space of the weak solutions of a family of linear spdes on one hand and the dirichlet space generated by the symmetrization of x on the other hand we study mainly linear equations in order to present the local time correspondence at a modest technical level however some of our work has consequences for nonlinear spdes as well we demonstrate this assertion by studying a family of parabolic spdes that have additive nonlinearities for those equations we prove that if the linearized problem has a random field solution then so does the nonlinear spde moreover the solution to the linearized equation is holder continuous if and only if the solution to the nonlinear equation is and the solutions are bounded and unbounded together as well finally we prove that in the cases that the solutions are unbounded they almost surely blow up at exactly the same points date october 7 2007 2000 mathematics subject classification primary 60h15 60j55 secondary 35r60 35d05

how often do simple dynamical processes have infinitely many coexisting sinks this work concerns the nature of chaotic dynamical processes sheldon newhouse wrote on dynamical processes depending on a parameter xx 1 t xn wherex is in the plane such as might arise when studying poincare return maps for autonomous differential equations in ir3 he proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane and that such parameter values would be dense in some interval the fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes we prove for an apparently typical situation that newhouse s construction yields only a set of parameter values of measure zero

basic control for the viscous moore greitzer partial differential equation the notions of basic controllability and basic control are defined a quadratic optimal control of the linearized viscous moore greitzer equation is presented and it is confirmed that stall is uncontrollable in this model a basic control is constructed for the nonlinear viscous moore greitzer equation which can control both surge and stall some extensions of this construction are discussed numerical simulations of the basic control are presented and its performance is compared to the performance of a backstepping control constructed by banaszuk hauksson and mezic siam j control optim 37 1999 pp 1503 1537 it is shown that the viscous moore greizer equation with throttle control is not basically controllable but under certain conditions adding air injection control will make the equation basically controllable

prevalence a translation invariant almost every on infinite dimensional spaces we present a measure theoretic condition for a property to hold almost everywhere on an infinite dimensional vector space with particularemphasis on function spaces such as c k and l p like the concept of lebesgue almost every on an infinite dimensional spaces our notion of prevalence is translation invariant instead of using a specific measure on the entire space we define prevalence in terms of the class of all probability measures with compact support prevalence is a more appropriate condition than the topological concepts of open and dense or generic when one desires a probabilistic result on the likelihood of a given property on a function space

closed form solution of visual inertial structure from motion this paper investigates the visual inertial structure from motion problem a simple closed form solution to this problem is introduced special attention is devoted to identify the conditions under which the problem has a finite number of solutions specifically it is shown that the problem can have a unique solution two distinct solutions and infinite solutions depending on the trajectory on the number of point features and on their layout and on the number of camera images the investigation is also performed in the case when the inertial data are biased showing that in this latter case more images and more restrictive conditions on the trajectory are required for the problem resolvability

an efficient solution to the five point relative pose problem an efficient algorithmic solution to the classical five point relative pose problem is presented the problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points the algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and subsequently finding its roots it is the first algorithm well suited for numerical implementation that also corresponds to the inherent complexity of the problem we investigate the numerical precision of the algorithm we also study its performance under noise in minimal as well as overdetermined cases the performance is compared to that of the well known 8 and 7 point methods and a 6 point scheme the algorithm is used in a robust hypothesize and test framework to estimate structure and motion in real time with low delay the real time system uses solely visual input and has been demonstrated at major conferences

brownian motion on the sierpinski gasket we construct a brownian motion taking values in the sierpinski gasket a fractal subset of 2 and study its properties this is a diffusion process characterized by local isotropy and homogeneity properties we show for example that the process has a continuous symmetric transition density p t x y with respect to an appropriate hausdorff measure and obtain estimates on p t x y

approximation of the semigroup generated by the robin laplacian in terms of the gaussian semigroup we consider the laplacian r subject to robin boundary conditions u u 0 on the space c where is a smooth bounded open subset of rn it is known that r generates an analytic contraction semigroup we show how this semigroup can be obtained from the gaussian semigroup on c0 rn via a trotter formula as the main ingredient we construct a positive contractive linear extension operator e from c to c0 rn which maps an operator core for r into the domain of the generator of the gaussian semigroup

genericity and robustness of full surplus extraction we study whether priors that admit full surplus extraction fse are generic an issue that becomes a gauge to evaluate the validity of the current mechanism design paradigm we consider the space of priors on the universal type space and thereby relax the assumption of a fixed finite number of types made by cremer and mclean 1988 we show that fse priors are topologically generic contrary to the result of heifetz and neeman 2006 that fse is generically impossible both geometrically and measure theoretically instead of using the bdp approach or convex combinations of priors adopted in heifetz and neeman 2006 we prove our genericity results by showing a robustness property of cremer mclean mechanisms

a generalization of sectorial and quasi sectorial operators abstract in the paper we generalize the main results presented in bentkus and paulauskas 2004 2 by giving rates of approximation of some semigroups of operators of the order n 0 1 also two classes of operators generalizing sectorial and quasi sectorial operators are introduced and their properties are studied

on equivalence of lp norms related to schrodinger type operators on riemannian manifolds in this paper we study schrodinger type operator on a riemannian manifold under some assumptions on a potential function we characterize the domain of the square root of the schrodinger type operator on l p space in the proof the defective intertwining properties and the littlewood paley inequalities play important roles

in defense of the eight point algorithm the fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras and the eight point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches it has the advantage of simplicity of implementation the prevailing view is however that it is extremely susceptible to noise and hence virtually useless for most purposes this paper challenges that view by showing that by preceding the algorithm with a very simple normalization translation and scaling of the coordinates of the matched points results are obtained comparable with the best iterative algorithms this improved performance is justified by theory and verified by extensive experiments on real images

probability of local bifurcation type from a fixed point a random matrix perspective results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems real random matrices time delay dynamical systems companion matrices and a set of mappings known for their properties as universal approximators neural networks the eigenvalue spectrum is considered both numerically and analytically using previous work of edelman et al based upon the numerical evidence various conjectures are presented the conclusion is that in many circumstances most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues nevertheless surprising situations are presented for which the aforementioned conclusion does not hold e g real random matrices with gaussian elements with a large positive mean and finite variance

on the error estimate of the integral kernel for the trotter product formula for schrodinger operators the error estimate of the integral kernel for the trotter product formula for schrodinger operators is shown a basic tool for doing so is the feynman kac formula based on the pinned brownian motion this formula enables us to express the integral kernel in handleable form and hence estimate it as a consequence the trotter product formula in the l p operator norm is obtained

an approximation to wiener measure and quantization of the hamiltonian on manifolds with non positive sectional curvature this paper gives a rigorous interpretation of a feynman path integral on a riemannian manifold m with non positive sectional curvature an l2 riemannian metric gp is given on the space of piecewise geodesic paths hp m adapted to the partition p of 0 1 whence a finite dimensional approximation of wiener measure is developed it is proved that as mesh p 0 the approximate wiener measure converges in an l1 sense to the measure exp 2 3203 01scal s ds d on the wiener space w m with wiener measure this gives a possible prescription for the path integral representation of the quantized hamiltonian as well as yielding such a result for the natural geometric approximation schemes originating in andersson and driver 1999 3 and followed by lim 2007 34

on lp contractivity of semigroups generated by linear partial differential operators abstract this paper is devoted to the study of contraction semigroups generated by linear partial differential operators it is shown that linear partial differential operators of order higher than two cannot generate contraction semigroups on l p n for p 1 unless p 2 if p 1 and the l p dissipativity criterion is restricted to the cone of nonnegative functions for differential operators with real valued coefficients it is proven that the criterion still fails for operators of order higher than two except for some fourth order operators if 3 2 p 3 a class of such fourth order operators is also presented

trotter kato product formula and fractional powers of self adjoint generators let a and b be non negative self adjoint operators in a hilbert space such that their densely defined form sum h a b obeys dom h dom a dom b for some 1 2 1 it is proved that if in addition a and b satisfy dom a1 2 dom b1 2 then the symmetric and non symmetric trotter kato product formula converges in the operator norm e tb 2ne ta ne tb 2n n e th o n 2 1 e ta ne tb n n e th o n 2 1 uniformly in t 0 t 0 t as n both with the same optimal error bound the same is valid if one replaces the exponential function in the product by functions of the kato class that is by real valued borel measurable functions f defined on the non negative real axis obeying 0 f x 1 f 0 1 and f 0 1 with some additional smoothness property at zero the present result improves previous ones relaxing the smallness of b with respect to a to the milder assumption dom a1 2 dom b1 2 and extending essentially the admissible class of kato functions

advanced topology on the multiscale sequence spaces s nu abstract we pursue the study of the multiscale spaces s introduced by jaffard in the context of multifractal analysis we give the necessary and sufficient condition for s to be locally p convex and exhibit a sequence of p norms that defines its natural topology the strong topological dual of s is identified to another sequence space depending on endowed with an inductive limit topology as a particular case we describe the dual of a countable intersection of besov spaces

numerical range and quasi sectorial contractions we apply a method developed by one of the authors see cite arl1 to localize the numerical range of textit quasi sectorial contractions semigroups our main theorem establishes a relation between the numerical range of quasi sectorial contraction semigroups exp t s t ge 0 and the maximal sectorial generators s we also give a new prove of the rate o 1 n for the operator norm euler formula approximation exp t s lim limits n to infty i ts n n t ge 0 for this class of semigroups

analyticity and discrete maximal regularity on lp spaces abstract in the first part of this paper we give the following interpolation result on the analyticity i e the property t i tn c n for all n n of an operator t on lp if t is powerbounded on lp and lq as well as analytic on lp then t is powerbounded and analytic on lr for all r strictly between p and q this is a discrete analogue of the well known corresponding result for analytic semigroups eta as recently shown by the author the analyticity of t is a necessary condition for the maximal regularity of the discrete time evolution equation un 1 tun fn for all n z u0 0 in the second part of this paper we establish the following two sufficient conditions for its maximal regularity t is a subpositive analytic contraction or t is an integral operator satisfying certain poisson bounds these results are discrete analogues of the corresponding results for the maximal regularity of the evolution equation u t au t f t for all t r u 0 0 due to lamberton weis coulhon and duong and hieber and pruss for the poisson bound result of coulhon and duong and hieber and pruss we give a slight improvement and a short proof

operator norm approximation of semigroups by quasi sectorial contractions abstract we extend the chernoff theory of approximation of contraction semigroups a la trotter we show that the trotter neveu kato convergence theorem holds in operator norm for a family of uniformly m sectorial generators in a hilbert space then we obtain a chernoff type approximation theorem for quasi sectorial contractions on a hilbert space in the operator norm we give necessary and sufficient conditions for the operator norm convergence of trotter type product formulae

homography based egomotion estimation with a common direction in this paper we explore the different minimal solutions for egomotion estimation of a camera based on homography knowing the gravity vector between calibrated images these solutions depend on the prior knowledge about the reference plane used by the homography we then demonstrate that the number of matched points can vary from two to three and that a direct closed form solution or a grobner basis based solution can be derived according to this plane many experimental results on synthetic and real sequences in indoor and outdoor environments show the efficiency and the robustness of our approach compared to standard methods

abundance of fast growth of the number of periodic points in 2 dimensional area preserving dynamics we prove that there exists an open subset of the set of real analytic hamiltonian diffeomorphisms of the two dimensional torus in which diffeomorphisms exhibiting fast growth of the number of periodic points are dense we also prove that there exists an open subset of the set of smooth area preserving diffeomorphisms of a closed surface in which typical diffeomorphisms exhibit fast growth of the number of periodic points

unbounded bivariant k theory and correspondences in noncommutative geometry by adapting the algebraic notion of universal connection to the setting of unbounded kk cycles we show that the kasparov product of such cycles can be defined directly by an algebraic formula in order to achieve this it is necessary to develop a framework of smooth algebras and a notion of differentiable c module the theory of operator spaces provides the required tools finally the above mentioned kk cycles with connection can be viewed as the morphisms in a category whose objects are spectral triples

wild hyperbolic sets yet no chance for the coexistence of infinitely many klus simple newhouse attracting sets the phenomenon of the coexistence of infinitely many sinks for two dimensional dissipative diffeomorphisms is a result due to newhouse ne1 ne2 in fact for each parameter value at which a homoclinic tangency is formed nondegenerately there exist intervals in the parameter space containing dense sets of parameter values for which there are infinitely many coexisting sinks robinson r the structure of the sinks constructed by newhouse is limited simple newhouse parameter values are values at which there are infinitely many sinks having some special well defined property concerning the structure a result due to tedeschini lalli and yorke ty says that the lebesgue measure of the set of simple newhouse parameter values is zero when the tangencies are due to the standard affine horseshoe map it is argued in ty and pr that a more general derivation of this measure zero result would be desirable the main result of this paper is that the lebesgue measure of the set of klus simple parameter values including the simple newhouse parameter values is zero for saddle hyperbolic basic sets forming tangencies

on the continuity of local times of borel right markov processes the problem of finding a necessary and sufficient condition for the continuity of the local times for a general markov process is still open barlow and hawkes have completely treated the case of the levy processes and marcus and rosen have solved the case of the strongly symmetric markov processes we treat here the continuity of the local times of borel right processes our approach unifies that of barlow and hawkes and of marcus and rosen by using an associated gaussian process that appears as a limit in a clt involving the local time process

strong uniqueness for both dirichlet operators and stochastic dynamics to gibbs measures on a path space with exponential interactions abstract we prove l p uniqueness of dirichlet operators for gibbs measures on the path space c r r d associated with exponential type interactions in infinite volume by extending an spde approach presented in previous work by the last two named authors we also give an spde characterization of the corresponding dynamics in particular for the first time we prove existence and uniqueness of a strong solution for the spde though the self interaction potential is not assumed to be differentiable hence the drift is possibly discontinuous as examples to which our results apply we mention the stochastic quantization of p 1 exp 1 and trigonometric quantum fields in infinite volume in particular our results imply essential self adjointness of the generator of the stochastic dynamics for these models finally as an application of the strong uniqueness result for the spde we prove some functional inequalities for diffusion semigroups generated by the above dirichlet operators

defective intertwining property and generator domain abstract we discuss the defective intertwining property of generators of semigroups we give some equivalent conditions in terms of generator resolvent and semigroup as an application using this property we give an example in which we can determine the exact generator domain of a schrodinger operator

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

on the character of convergence to brownian local time ii in this paper we consider the sequences of stochastic processes which converge weakly asn to brownian local time these processes are generated by a recurrent random walk with finite variance the main result is the following it is possible to redefine a random walk in such a way that for a wide class of processes the normalized differences between them and brownian local time converge in distribution to some stochastic process we also prove that such differences with probability one have the logarithmic upper bound it is so called strong invariance principles for local times

bifurcation to infinitely many sinks this paper considers one parameter families of diffeomorphisms ft in two dimensions which have a curve of dissipative saddle periodic pointspt i e ftn pt pt and detdftn pt 1 the family is also assumed to create new homoclinic intersections of the stable and unstable manifolds ofpt as the parameter varies throught0 gavirlov and silnikov proved that if the new homoclinic intersections are created nondegenerately att0 then there is an infinite cascade of periodic sinks i e there are parameter valuestn accumulating att0 for which there is a sink of periodn gs2 sect 4 we show that this result is true for real analytic diffeomorphisms even if the homoclinic intersection is created degenerately we give computer evidence to show that this latter result is probably applicable to the henon map fora near 1 392 andb equal 0 3