Related papers: Topological Stability and Shadowing in Uniform Tra…

We investigate expansiveness, topological stability, and shadowing for continuous actions of semigroups on compact Hausdorff spaces. We characterize semigroups for which all full shifts are expansive. We show that every expansive continuous…

In this paper we extend to an infinite dimensional setting some results on the shadowing property that are known on finite dimensional compact manifolds without border and in $\mathbb{R}^n$. In fact, we show that if $\{\T(t):t\ge 0\}$ is a…

We extend the notions of topological stability, shadowing and persistence from homeomorphisms to finitely generated group actions on uniform spaces and prove that an expansive action with either shadowing or persistence is topologically…

We study iterated function systems (IFS) with compact parameter space. We show that the space of IFS with phase space $X$ is the hyperspace of the space of self continuous maps of $X$. With this result we obtain that the Hausdorff distance…

We find sufficient conditions for commutative non-autonomous systems on certain metric spaces to be topologically stable. In particular, we prove that (i) Every mean equicontinuous, mean expansive system with strong average shadowing…

The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…

In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we…

We study expansivity and the shadowing property for finitely generated group actions on metric spaces. We consider the projecting and lifting problems for actions having these properties. We prove that every expansive action with the…

For topological dynamical systems defined by continuous self-maps of compact metric spaces, we consider the contractive shadowing property, i.e., the Lipschitz shadowing property such that the Lipschitz constant is less than 1. We prove…

We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for…

This paper aims at formulating definitions of topological stability, structural stability, and expansiveness property for an iterated function system( abbrev, IFS). It is going to show that the shadowing property is necessary condition for…

We relate stability properties (i.e. moment exponents) of a stochastic dynamical system on a compact manifold $M$ to the homotopy and integral homology groups of $M$. In the special case of gradient Brownian systems associated to isometric…

We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…

We point out a basic dichotomy between the shadowing and Lipschitz shadowing properties for one-sided shift spaces in two infinite-alphabet frameworks: the classical product-topology model $X\subseteq A^{\mathbb{N}}$ and the compact…

We define the concept of $(\mathscr{F},\mathscr{G})-$shadowing property on uniform space and say it as a topological $(\mathscr{F},\mathscr{G})-$shadowing property. We show that topological shadowing, topological…

In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property then…

This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup…

In this paper, we study dynamical properties as shadowing and structural stability for a class of dynamics on $\mathbb{Z}_p$ and $\mathbb{Q}_p$, where $p \geq 2$ is a prime number. In particular, we prove that if $f: \mathbb{Z}_p \to…

Let $\tilde{G}$ be a finite group, $G$ a normal subgroup of $\tilde{G}$ and $k$ an algebraically closed field of characteristic $p>0$. The first main result in this paper is to show that support $\tau$-tilting $k\tilde{G}$-modules…

This Part establishes the geometric theory of uniformly hyperbolic sets with explicit quantitative bounds throughout, and contains five main theorems. The Stable Manifold Theorem is proved via the backward graph transform, with a complete…