Lyapunov Functions and Cone Families
AbstractWe describe systematically the relation between Lyapunov functions and nonvanishing Lyapunov exponents, both for maps and flows. This includes a brief survey of the existing results in the...
View ArticleCharacterization of strong exponential dichotomies
AbstractWe introduce the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility of bounded solutions. The latter refers...
View ArticleOn a Question by Markus Seidel
AbstractWe give necessary and sufficient conditions for the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication and...
View ArticleA note on the theorem of Johnson, Palmer and Sell
AbstractThe well-known theorem of Johnson, Palmer and Sell asserts that the endpoints of the Sacker–Sell spectrum of a given cocycle \(\mathcal {A}\) over a topological dynamical system (M, f) are...
View ArticleNonuniform exponential dichotomies and Lyapunov functions
AbstractFor the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential...
View ArticleOptimal Linear Responses for Markov Chains and Stochastically Perturbed...
AbstractThe linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an...
View ArticleA version of the theorem of Johnson, Palmer, and Sell for quasicompact cocycles
AbstractThe well-known theorem of Johnson, Palmer, and Sell asserts that the endpoints of the Sacker–Sell spectrum of a given cocycle of invertible matrices over a topological dynamical system (M, f)...
View ArticleSmooth linearization of nonautonomous difference equations with a nonuniform...
AbstractThere have been obtained many results on smooth linearization for diffeomorphisms, those results cannot be simply applied to nonautonomous difference equations. In this paper we investigate...
View ArticleStability and Approximation of Statistical Limit Laws for Multidimensional...
AbstractThe unpredictability of chaotic nonlinear dynamics leads naturally to statistical descriptions, including probabilistic limit laws such as the central limit theorem and large deviation...
View ArticleOn Stability of Discrete Dynamical Systems: From Global Methods to Ergodic...
AbstractThe aim of this paper is to give a complete description of the input–output methods for uniform exponential stability of discrete dynamical systems. We present a new study from four...
View ArticleLimit Theorems for Random Expanding or Anosov Dynamical Systems and...
AbstractThe purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic (Anosov) dynamics developed by the first author et al. to...
View ArticleOn the Hyers–Ulam stability of certain nonautonomous and nonlinear difference...
AbstractThis article is devoted to the study of certain nonautonomous and nonlinear difference equations of higher order. Our main objective is to formulate sufficient conditions under which the class...
View ArticleHyers–Ulam Stability for Nonautonomous Semilinear Dynamics on Bounded Intervals
AbstractWe prove that any nonautonomous semilinear dynamics on a bounded interval with the property that the nonlinear part is Lipschitz with a sufficiently small Lipschitz constant exhibits Hyers–Ulam...
View ArticleHyers–Ulam Stability for a Class of Perturbed Hill’s Equations
AbstractIn this note we formulate sufficient conditions under which a certain class of nonlinear and nonautonomous differential equations of second order is Hyers–Ulam stable. This class consists of...
View ArticleAlmost Sure Invariance Principle for Random Distance Expanding Maps with a...
AbstractWe prove a quenched almost sure invariance principle for certain classes of random distance expanding dynamical systems which do not necessarily exhibit uniform decay of correlations.
View ArticleA generalized Grobman–Hartman theorem for nonautonomous dynamics
AbstractThe purpose of this note is to extend the recent generalized version of the Grobman–Hartman theorem established by Bernardes Jr. and Messaoudi from an autonomous to nonautonomous dynamics. More...
View ArticleShadowing for nonautonomous and nonlinear dynamics with impulses
AbstractFor a large class of nonautonomous semilinear impulsive differential equations, we formulate sufficient conditions under which in a vicinity of each approximate solution, we can construct an...
View ArticleBosnia and Herzegovina After the Transition: Forever Postwar, Postsocialist...
AbstractThe paper brings together several strands of academic and activist involvement with Bosnia and Herzegovina’s (BiH) colonial, postwar and postsocialist condition including relevant theoretical...
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