non uniform specification and large deviations for weak gibbs measures we establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak gibbs measures under some mild assumptions we obtain upper and lower bounds for the measure of deviation sets of some non uniformly expanding maps including quadratic maps and robust multidimensional non uniformly expanding local diffeomorphisms for that purpose a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non uniformly expanding local diffeomorphisms and viana maps

covering relations for multidimensional dynamical systems abstract we present a topological technique for analyzing dynamical systems with complex behavior based on the general notion of covering relations our method can be used to study multidimensional dynamical systems with an arbitrary number of topologically expanding directions

a new dissipative time stepping algorithm for frictional contact problems formulation and analysis this paper presents a new time stepping algorithm for frictional contact problems that exhibits unconditional positive energy dissipation more specifically the proposed scheme preserves a priori stability estimates of the continuum problem for both frictionless and frictional contact leading to improved numerical stability properties in particular for the normal contact component the algorithm exhibits full energy conservation between released states while the energy does not increase over its initial value due to the enforcement of the normal contact constraint during persistent contact a penalty regularization is considered to this purpose a new regularization of the stick conditions is considered for the frictional part the new scheme is shown rigorously to exhibit positive energy dissipation like the continuum physical problem in this frictional case coulomb friction is assumed complete analyses of these considerations as well as a detailed description of their finite element implementation are included in the general finite deformation range representative numerical simulations are presented to assess the performance of the newly proposed methods

entropy and data compression schemes some new ways of defining the entropy of a process by observing a single typical output sequence as well as a new kind of shannon mcmillan breiman theorem are presented this provides a new and conceptually very simple ways of estimating the entropy of an ergodic stationary source as well as new insight into the workings of such well known data compression schemes as the lempel ziv algorithm

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

approximation properties on invariant measure and oseledec splitting in non uniformly hyperbolic systems we prove that each invariant measure in a non uniformly hyperbolic system can be approximated by atomic measures on hyperbolic periodic orbits this contributes to our main result that the mean angle definition 1 10 independence number definition 1 6 and oseledec splitting for an ergodic hyperbolic measure with simple spectrum can be approximated by those for atomic measures on hyperbolic periodic orbits respectively combining this result with the approximation property of lyapunov exponents by wang and sun 2005 theorem 1 9 we strengthen katok s closing lemma 1980 by presenting more extensive information not only about the state system but also its linearization in the present paper we also study an ergodic theorem and a variational principle for mean angle independence number and liao s style number definition 1 3 which are bases for discussing the approximation properties in the main result

on contact anosov flows exponential decay of correlations for co 4 contact anosov flows is established this implies in particular exponential decay of correlations for all smooth geodesic flows in strictly negative curvature

zero entropy dynamical systems with the gluing orbit property abstract under the assumption of the gluing orbit property equivalent conditions to having zero topological entropy are investigated in particular we show that a dynamical system has the gluing orbit property and zero topological entropy if and only if it is minimal and equicontinuous

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

multifractal analysis of hyperbolic flows we establish the multifractal analysis of hyperbolic flows and of suspension flows over subshifts of finite type a non trivial consequence of our results is that for every holder continuous function non cohomologous to a constant the set of points without birkhoff average has full topological entropy

topological features of flows with the reparametrized gluing orbit property abstract the notions of shadowing specification and gluing orbit property differ substantially for discrete and continuous time dynamical systems in the present paper we continue the study of the topological and ergodic properties of continuous flows with the reparametrized periodic and nonperiodic gluing orbit properties initiated in 3 we prove these flows satisfy a weak mixing condition with respect to balls and if the flow is komuro expansive the topological entropy is a lower bound for the exponential growth rate of periodic orbits moreover we show that periodic measures are dense in the set of all invariant probability measures and that ergodic measures are generic furthermore we prove that irrational rotations and some minimal flows on tori and circle extensions over expanding maps satisfy gluing orbit properties thus emphasizing the difference of this property with respect the notion of specification

stability of mixing and rapid mixing for hyperbolic flows we obtain general results on the stability of mixing and rapid mixing superpolynomial decay of correlations for hyperbolic flows amongst c r axiom a flows r 2 we show that there is a c 2 open c r dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing this is the first general result on the stability of rapid mixing or even mixing for axiom a

on the numerical implementation of inelastic time dependent and time independent finite strain constitutive equations in structural mechanics abstract a number of complex issues are resolved in a way that allows the incorporation of finite strain inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics without recourse to extensive continuum mechanics preliminaries an elementary time independent plasticity model an elementary time dependent creep model and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations the constitutive equations are all suitable for problems involving large deformations and finite strains the plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co rotational time derivative of the cauchy stress the viscoelastic model computes the current value of the cauchy stress from a hereditary integral of a materially invariant form of the stretching history the current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration the process of strain incrementation is examined in some depth the stretching evaluated at the mid interval and multiplied by the time step is identified as the appropriate finite strain increment to use with the selected forms of the constitutive equations discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations these rotations are used to update stresses and state variables due to rigid body rotation during the load increment comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately if not exactly for any time step and stretching this material taken collectively provides an approach to numerical implementation which is marked by its simplicity

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

thermodynamics of towers of hyperbolic type we introduce a class of continuous maps f of a compact topological space x admitting inducing schemes of hyperbolic type and describe the associated tower constructions we then establish a thermodynamic formalism i e we describe a class of real valued potential functions on x such that f possess a unique equilibrium measure associated to each which minimizes the free energy among the measures that are liftable to the tower we also describe some ergodic properties of equilibrium measures including decay of correlations and the central limit theorem we then study the liftability problem and show that under some additional assumptions on the inducing scheme every measure that charges the base of the tower and has sufficiently large entropy is liftable our results extend those obtained in ps05 ps08 for inducing schemes of expanding types and apply to certain multidimensional maps applications include obtaining the thermodynamic formalism for young s diffeomorphisms the henon family at the first birfucation and the katok map in particular for the katok map we obtain the exponential decay of correlations for equilibrium measures associated to the geometric potentials with 0 t 1

large deviations for nonuniformly hyperbolic systems we obtain large deviation estimates for a large class of nonuniformly hyperbolic systems namely those modelled by young towers with summable decay of correlations in the case of exponential decay of correlations we obtain exponential large deviation estimates given by a rate function in the case of polynomial decay of correlations we obtain polynomial large deviation estimates and exhibit examples where these estimates are essentially optimal in contrast with many treatments of large deviations our methods do not rely on thermodynamic formalism hence for holder observables we are able to obtain exponential estimates in situations where the space of equilibrium measures is not known to be a singleton as well as polynomial estimates in situations where there is not a unique equilibrium measure

some computational aspects of large deformation rate dependent plasticity problems abstract the governing equations for a finite element formulation of boundary value problems for large deformation metal forming processes are derived using a principle of virtual work formulated in a lagrangian reference system the updated lagrangian method is used to simplify the equations the resulting nonlinear equilibrium equations are solved using newton s method a constitutive model for large deformation rate dependent plasticity is developed the model incorporates a one parameter implicit integration operator for stability and accuracy the stressrate strain rate relation is written in terms of the jaumann rate of stress numerous example problems are solved to demonstrate the effectiveness of the numerical algorithms

billiards in polygons survey of recent results in the ten or so years since the publication of ref 19 polygonal billiards have remained an active subject of research in the mathematics and physics literature as a result our understanding of the subject although still far from being complete is much better than it was ten years ago this survey attempts to give a broad overview of the dynamics of billiards in polygons with an emphasis on the material that was not in the literature in 1985 this is not a survey of the publications on polygonal billiards and we apologize to authors whose work has not been included the selection of topics has been strongly influenced by the personal taste of the author and by space limitations thus we do not discuss quantum polygonal billiards in particular quantum chaos see e g refs 41 44 and 45 we hope that somebody will write a survey on this important subject in the near future a fascinating aspect of the subject is the interplay between the geometric shape of the billiard table i e a planar curve and the qualitative features of the billiard dynamics hence it is instructive to compare polygonal billiard tables with other classes of billiard tables in particular the smooth strictly convex tables and the dispersing or sinai tables produce strikingly different types of billiard dynamics we recommend refs 46 and 15 for a general overview of the subject and a comparative study of billiard dynamics for various types of billiard tables

lipschitz flow box theorem abstract a generalization of the flow box theorem is proven the assumption of a c 1 vector field f is relaxed to the condition that f be locally lipschitz continuous the theorem holds in any banach space

vector fields with topological stability in this paper we give a characterization of the structurally stable vector fields by making use of the notion of topological stability more precisely it is proved that the c1 interior of the set of all topologically stable c1 vector fields coincides with the set of all vector fields satisfying axiom a and the strong transversality condition

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

persistent stability of a chaotic system abstract we report that trajectories of a one dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time despite the fact that the system is chaotic we provide a detailed quantitative description of this effect by developing the large deviation theory for fluctuations of the finite time lyapunov exponent of this system specifically the determination of the entropy function for the distribution reduces to the analysis of a schrodinger equation which is tackled by semi classical methods the system has generic instability properties and we consider the broader implications of our observation of long term stability in chaotic systems

specification and towers in shift spaces we show that a shift space on a finite alphabet with a non uniform specification property can be modeled by a strongly positive recurrent countable state markov shift to which every equilibrium state lifts in addition to uniqueness of the equilibrium state this gives strong statistical properties including the bernoulli property exponential decay of correlations central limit theorem and analyticity of pressure which are new even for uniform specification we give applications to shifts of quasi finite type synchronised and coded shifts and factors of beta shifts and s gap shifts

advection diffusion equation with absorbing boundary we consider a spatially homogeneous advection diffusion equation in which the diffusion tensor and drift velocity are time independent but otherwise general we derive asymptotic expressions valid at large distances from a steady point source for the flux onto a completely permeable boundary and onto an absorbing boundary the absorbing case is treated by making a source of antiparticles at the boundary this method is more general than the method of images in both cases there is an exponential decay as the distance from the source increases we find that the exponent is the same for both boundary conditions

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

power law distributions of particle concentration in free surface flows particles floating on the surface of a turbulent incompressible fluid accumulate along string like structures while leaving large regions of the flow domain empty this is reflected experimentally by a very peaked probability distribution function of c r the coarse grained particle concentration at scale r around c r 0 with a power law decay over two decades of c r pi c r proportional variant c r beta r the positive exponent beta r decreases with scale in the inertial range and stays approximately constant in the dissipative range thus indicating a qualitative difference between the dissipative and the inertial ranges of scales also visible in the first moment of c r

the gluing orbit property uniform hyperbolicity and large deviations principles for semiflows abstract we introduce a gluing orbit property weaker than specification for both continuous maps and flows we prove that flows with the c 1 robust gluing orbit property are uniformly hyperbolic and that every uniformly hyperbolic flow satisfies the gluing orbit property we also prove a level 1 large deviations principle and a level 2 large deviations lower bound for semiflows with the gluing orbit property as a consequence we establish a level 1 large deviations principle for hyperbolic flows and every continuous observable and also a level 2 large deviations lower bound finally since many non uniformly hyperbolic flows can be modeled as suspension flows we also provide criteria for such flows to satisfy uniform and non uniform versions of the gluing orbit property

periodic billiard orbits are dense in rational polygons we show that periodic orbits are dense in the phase space for billiards in polygons for which the angle between each pair of sides is a rational multiple of 7r

nonsingular star flows satisfy axiom a and the no cycle condition we give an affirmative answer to a problem of liao and mane which asks whether for a nonsingular flow to loose the stability it must go through a critical element bifurcation more precisely a vector field s on a compact boundaryless manifold is called a star system if s has a c 1 neighborhood mathcal u in the set of c 1 vector fields such that every singularity and every periodic orbit of every x in mathcal u is hyperbolic we prove that any nonsingular star flow satisfies axiom a and the no cycle condition

a continuum based finite element formulation for the implicit solution of multibody large deformation frictional contact problems in this paper a formulation is presented for the finite element treatment of multibody large deformation frictional contact problems the term multibody is used to mean that when two bodies mechanically contact both may be deformable a novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first before deriving the corresponding finite element equations this feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general in particular the approach yields a characterization of the frictional constraint assuming a coulomb law suitable for arbitrary discretizations in either two or three dimensions a geometric framework is constructed within which both frictionless and frictional response are naturally described making subsequent finite element discretization a straightforward substitution of finite dimensional solution spaces for their continuum counterparts to our knowledge this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature the development includes exact linearization of the statement of virtual work which enables optimal convergence properties for newton raphson solution strategies and which appears to be highly desirable if not essential for the general robustness of implicit finite element techniques since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non linear behaviour this assertion is substantiated through presentation of a variety of examples in both two and three dimensions

b expansions and symbolic dynamics given a real number p i it is easy to expand x e o i in a canonical way into a series of negative powers of p with integer coefficients less than or equal to p the form of the set of such p expansions which is a matter of symbolic dynamics or language theory varies according to arithmetical properties of p but there are many common features known facts which are few and open questions much more numerous are reviewed in this paper

the specification property for flows from the robust and generic viewpoint abstract we prove that if x has the weak specification property robustly where is an isolated set then is a hyperbolic topologically mixing set and as a consequence if x is a vector field that has the weak specification property robustly on a closed manifold m then the flow x t is a topologically mixing anosov flow also we prove that there exists a residual subset r x 1 m so that if x r and x has the weak specification property then x t is an anosov flow

the entropy theory of symbolic extensions fix a topological system x t with its space k x t of t invariant borel probabilities if y s is a symbolic system subshift and y s x t is a topological extension factor map then the function h ext on k x t which assigns to each the maximal entropy of a measure on y mapping to is called the extension entropy function of the infimum of such functions over all symbolic extensions is called the symbolic extension entropy function and is denoted by h sex in this paper we completely characterize these functions in terms of functional analytic properties of an entropy structure on x t the entropy structure is a sequence of entropy functions h k defined with respect to a refining sequence of partitions of x or of x z for some auxiliary system z r with simple dynamics whose boundaries have measure zero for all the invariant borel probabilities we develop the functional analysis and computational techniques to produce many dynamical examples for instance we resolve in the negative the question of whether the infimum of the topological entropies of symbolic extensions of x t must always be attained and we show that the maximum value of h sex need not be achieved at an ergodic measure we exhibit several characterizations of the asymptotically h expansive systems of misiurewicz which emerge as a fundamental natural class in the context of the entropy structure the results of this paper are required for the downarowicz newhouse results dn on smooth dynamical systems

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

equivalence of gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification letm be a compact metrizable space f m m a homeomorphism satisfying expansiveness and specification anda m a function such that left sum limits k 0 n 1 a f k x a f k y right mathbin lower 3ex hbox buildrel over smash scriptstyle vphantom x k varepsilon infty whenevern 1 andx y are e n close i e d fkx fky 0 under these conditions bowen has shown that there is a uniqueequilibrium state fora assuming thatk 0 when 0 we show that is also the uniquegibbs state fora we further definequasi gibbs states and show that is the uniquef invariant quasi gibbs state fora

on intrinsic ergodicity and weakenings of the specification property abstract since seminal work of bowen 2 it has been known that the specification property implies various useful properties about an expansive topological dynamical system among them uniqueness of the measure of maximal entropy often referred to as intrinsic ergodicity weakenings of the specification property have been defined and profitably applied in various works such as 6 9 11 16 17 it has been an open question see p 798 of 4 whether two of these properties which we here call almost specification and non uniform specification imply intrinsic ergodicity for expansive topological systems we answer this question negatively by exhibiting examples of subshifts with multiple measures of maximal entropy with disjoint support which have non uniform specification with any gap function f n o ln n or almost specification with any mistake function g n 4 we also show some results in the opposite direction showing that subshifts with non uniform specification with gap function f n o ln n or almost specification with mistake function g n 1 cannot have multiple measures of maximal entropy with disjoint support

some large deviation results for dynamical systems we prove some large deviation estimates for continuous maps of compact metric spaces and apply them to attractors in differentiable dynamics rate of escape problems and to shift spaces

applying nagata patches to smooth discretized surfaces used in 3d frictional contact problems the accurate solution of large deformation frictional contact problems using the finite element method is still a challenging task due to the strong nonlinearities involved this paper presents a smoothing method applicable to 3d contact surfaces discretized with an arbitrary mesh topology the quadratic nagata patch interpolation is adopted to define the smooth surface the resulting contact surface passes through all nodes of the mesh while providing a smooth description with at least g 1 continuity at the nodes and quasi g 1 continuity between the patches thus the proposed method avoids the non physical oscillations in the contact force which are induced by the traditionally used faceted contact surfaces description when slave nodes slide over several master segments moreover it allows the accurate evaluation of kinematic variables leading to important improvements in terms of convergence rate within the newton raphson iteration loop the developed global and local contact search algorithms designed for contact surfaces described by nagata patches are described in detail three numerical examples were selected to illustrate the advantages of the proposed smoothing method including a complex industrial example of sheet metal forming process the results show the significant improvements attained with the proposed approach in terms of efficiency robustness and accuracy when compared with the traditional faceted contact surfaces description 2014 published by elsevier b v

equilibrium states for impulsive semiflows abstract we consider impulsive semiflows defined on compact metric spaces and give sufficient conditions both on the semiflows and the potential functions for the existence and uniqueness of equilibrium states we also generalize the classical notion of topological pressure to our setting of discontinuous semiflows and prove a variational principle

objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses abstract computational techniques which preserve the objectivity of incremental constitutive relations for finite elastic or inelastic materials for finite time steps during which the material elements may undergo finite rotations are presented these techniques are useful in finite deformation finite rotations and finite strain computational analysis of two as well as three dimensional solids and structures

denseness of intermediate pressures for systems with the climenhaga thompson structures abstract we show that systems with the structure introduced by climenhaga and thompson have dense intermediate pressures and dense intermediate entropies of ergodic measures the result applies to the mane diffeomorphisms

on genericity of shadowing and periodic shadowing property abstract let m be a smooth compact manifold possibly with boundary or compact manifold with dim m 3 or dim m 6 we prove that generic homeomorphism on m has the periodic shadowing property

the mathematics of atmospheric dispersion modeling the gaussian plume model is a standard approach for studying the transport of airborne contaminants due to turbulent diffusion and advection by the wind this paper reviews the assumptions underlying the model its derivation from the advection diffusion equation and the key properties of the plume solution the results are then applied to solving an inverse problem in which emission source rates are determined from a given set of ground level contaminant measurements this source identification problem can be formulated as an overdetermined linear system of equations that is most easily solved using the method of least squares various generalizations of this problem are discussed and we illustrate our results with an application to the study of zinc emissions from a smelting operation

ergodic universality of some topological dynamical systems the krieger generator theorem says that every invertible ergodic measure preserving system with finite measure theoretic entropy can be embedded into a full shift with strictly greater topological entropy we extend krieger s theorem to include toral automorphisms and more generally any topological dynamical system on a compact metric space that satisfies almost weak specification asymptotic entropy expansiveness and the small boundary property as a corollary one obtains a complete solution to a natural generalization of an open problem in halmos s 1956 book regarding an isomorphism invariant that he proposed

on the periodic orbits shadowing and strong transitivity of continuous flows abstract we prove that chaotic flows i e flows that satisfy the shadowing property and have a dense subset of periodic orbits satisfy a reparametrized gluing orbit property similar to the one introduced in bomfim and varandas 2015 in particular these are strongly transitive in balls of uniform radius we also prove that the shadowing property for a flow and a generic time t map and having a dense subset of periodic orbits hold for a c 0 baire generic subset of lipschitz vector fields that generate continuous flows similar results also hold for c 0 generic homeomorphisms and in particular we deduce that chain recurrent classes of c 0 generic homeomorphisms have the gluing orbit property

unique equilibrium states for flows and homeomorphisms with non uniform structure abstract using an approach due to bowen franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the bowen property we show that this conclusion remains true using weaker non uniform versions of specification expansivity and the bowen property we also establish a corresponding result for homeomorphisms in the homeomorphism case we obtain the upper bound from the level 2 large deviations principle for the unique equilibrium state the theory presented in this paper provides the basis for an ongoing program to develop the thermodynamic formalism in partially hyperbolic and non uniformly hyperbolic settings

a matrix contraction process we consider a stochastic process in which independent identically distributed random matrices are multiplied and where the lyapunov exponent of the product is positive we continue multiplying the random matrices as long as the norm of the product is less than unity if the norm is greater than unity we reset the matrix to a multiple of the identity and then continue the multiplication we address the problem of determining the probability density function of the norm we argue that in the limit as where and are two real parameters our motivation for analysing this matrix contraction process is that it serves as a model for describing the fine structure of strange attractors where a dense concentration of trajectories results from the differential of the flow being contracting in some region we exhibit a matrix product model for the differential of the flow in a random velocity field and show that there is a phase transition with the parameter changing abruptly from to as a parameter of the flow field model is varied

the ale formulation of bodies in rolling contact theoretical foundations and finite element approach abstract numerical methods for the analysis of rolling contact problems are of high importance for the optimization of the components car tires for example today finite element methods for the computation of stationary rolling contact have been developed for industrial use however from a review of the scientific literature it has been concluded that the theoretical foundations of the relative kinematic description i e an arbitrary lagrangian eulerian ale formulation seems to be not well understood in detail this presentation is aimed to close this gap starting from the basic kinematic description of the ale formulation of rolling the weak form of the equations of motion are developed by this careful analysis an additional flux contribution is derived which has not been recognized in the scientific literature so far the contact problem is described for the treatment of two deformable bodies in rolling contact within the framework of well established methods for the numerical treatment of contact in the lagrangian picture in general essential differences between the lagrangian description and the ale description of rolling are shown up and discussed in detail for a comprehensive presentation the finite element discretization is restricted to the case of a deformable wheel rolling on a rigid plane surface however the sketched algorithmic approach is valid in general the efficiency of the numerical algorithms developed so far are discussed by the analysis of a simple three dimensional example critical remarks and an outlook to further research in this field concludes this presentation

natural equilibrium states for multimodal maps this paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps this class contains but it is larger than collet eckmann for a map in this class we prove existence and uniqueness of equilibrium states for the geometric potentials t log df for the largest possible interval of parameters t we also study the regularity and convexity properties of the pressure function completely characterising the first order phase transitions results concerning the existence of absolutely continuous invariant measures with respect to the lebesgue measure are also obtained

numerical integration of rate constitutive equations in finite deformation analysis abstract in analysis of finite deformation problems the use of constitutive equations in rate form is often required in a spatial setting these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation constitutive equations of this type characterize a variety of material models including hyperelasticity hypoelasticity and elastoplasticity employing geometrical concepts a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations these algorithms which are appropriate for finite deformation analysis are applicable to any choice of stress rate and in most cases employ quantities that arise naturally in the context of finite element analysis examples illustrate the objectivity and accuracy of the algorithms

the convected description in large deformation frictional contact problems abstract the converted description is introduced for finite deformation frictional contact problems such that both coulomb and more general friction criteria can be conveniently and reliably numerically implemented in lagrangian finite element calculations the discussion includes careful definition of the convected frame from the standpoint of differential geometry complete with physical interpretations of the frame and the associated slip and traction rate measures as demonstrated use of these measures enables prescription of frictional constitutive relationships with virtually no more complexity than is required by the kinematically linear theory while ensuring the required frame indifference of the description as a result the work provides a sound mathematical and continuum mechanical foundation for future implementations of general friction laws in large deformation solid mechanics computing architectures

non uniformly hyperbolic flows and shadowing abstract we consider a hyperbolic ergodic measure of a c 1 flow on a compact manifold under the hypothesis that there are no fixed points and that the oseledec splitting of the normal bundle satisfies a limit domination property we prove that the measure has a shadowing property as an application of this result we prove that the measure can be approached on the weak topology by measures supported on hyperbolic periodic orbits

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

measures of maximal entropy for suspension flows over the full shift we consider suspension flows with continuous roof function over the full shift sigma on a finite alphabet for any positive entropy subshift of finite type y subset sigma we explicitly construct a roof function such that the measure s of maximal entropy for the suspension flow over sigma are exactly the lifts of the measure s of maximal entropy for y in the case when y is transitive this gives a unique measure of maximal entropy for the flow which is not fully supported if y has more than one transitive component all with the same entropy this gives explicit examples of suspension flows over the full shift with multiple measures of maximal entropy this contrasts with the case of a holder continuous roof function where it is well known the measure of maximal entropy is unique and fully supported