Related papers: Topological entropy and recurrence properties in n…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
In our previous paper [9], we have introduced topological nearly entropy, Ent_N (f) by restricting X into a class of nearly compact spaces. In the present paper, some additional properties of this notion are studied. Furthermore, we…
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew \cite{AKM} to set-valued functions from a closed subset $A$ of the interval to closed subsets of the interval. We view these set-valued functions, via…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…
We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets of full topological entropy and full Hausdorff dimension. The examples include some partially hyperbolic systems and geometric Lorenz flows. We…
We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…
For a path-connected metric space $(X,d)$, the $n$-th homotopy group $\pi_n(X)$ inherits a natural pseudometric from the $n$-th iterated loop space with the uniform metric. This pseudometric gives $\pi_n(X)$ the structure of a topological…
Let $X$ be a compact metric space and $T:X\longrightarrow X$ be continuous. Let $h^*(T)$ be the supremum of topological sequence entropies of $T$ over all subsequences of $\mathbb Z_+$ and $S(X)$ be the set of the values $h^*(T)$ for all…
The Adler-Konheim-McAndrew type definitions and the Bowen-Dinaburg-Hood type definitions of parametric topological entropy will be considered on orbits and coincidence orbits of nonautonomous multivalued maps in compact Hausdorff spaces.…
In this article we study persistence features of topological entropy and periodic orbit growth of Hamiltonian diffeomorphisms on surfaces with respect to Hofer's metric. We exhibit stability of these dynamical quantities in a rather strong…
We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…
Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Let $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ be a sequence of continuous self-maps on a compact metric space $X$. The non-autonomous dynamical system $(X,f_{0,\infty})$ induces the set-valued system $(\mathcal{K}(X), \bar{f}_{0,\infty})$ and…
We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact…
The goal of this article is to study how combinatorial equivalence implies topological conjugacy. For that, we introduce the concept of kneading sequences for nonautonomous discrete dynamical systems and show that these sequences are a…
We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover,…
In this paper, we study the dynamics of a non-autonomous dynamical system $(X,\mathbb{F})$ generated by a sequence $(f_n)$ of continuous self maps converging uniformly to $f$. We relate the dynamics of the non-autonomous system…