Related papers: A note on sensitivity of semigroup actions

Topological dynamical systems $(X,T)$ are actions $T \times X \to X$, given as $(t, x) \to tx$, on a compact, Hausdorff topological space $X$ with $T$ as an acting group or monoid. We take up the property of topological transitivity…

Motivated by Furstenberg's Theorem on sets in the circle invariant under multiplication by a non-lacunary semigroup, we define a general class of dynamical systems possessing similar topological dynamical properties. We call such systems…

In this paper, we study properties of sensitivity, transitivity and chaos for non-autonomous discrete systems(NDS). Firstly, we present some different sufficient conditions for NDS to be chaotic. Then, we relate the transitivity with the…

Let $(X,T)$ be a topological dynamical system and $\mathcal{F}$ be a Furstenberg family (a collection of subsets of $\mathbb{Z}_+$ with hereditary upward property). A point $x\in X$ is called an $\mathcal{F}$-transitive one if…

This paper proves that a set-valued dynamical system is sensitively dependent on initial conditions (resp., $\mathscr{F}$-sensitive, multi-sensitive) if and only if its $g$-fuzzification is sensitively dependent on initial conditions…

In this article, we define amorphic complexity for actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $\mathbb Z$-actions, is a topological invariant which…

In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…

We show that the existence of a dense set of periodic points for a topologically transitive non-minimal continuous group action on a Hausdorff uniform space with an infinite acting group does not necessarily imply a sensitive dependence to…

In this work, we show that if $f$ is a uniformly continuous map defined over a Polish metric space, then the set of $f$-invariant measures with zero metric entropy is a $G_\delta$ set (in the weak topology). In particular, this set is…

In topological dynamics, the dynamical behavior sometimes has a sharp contrast when the action is by semigroups or monoids to when the action is by groups. In this article we bring out this contrast while discussing the equivalence of…

This paper's major purpose is to continue the work of Zhu and Ma[1]. To begin, the $\mathbf{g}$-almost product property, more general irregular and regular sets, and some new notions of the Banach upper density recurrent points and…

In this paper, we shall introduce $h$-expansiveness and asymptotical $h$-expansiveness for actions of sofic groups. By the definitions, each $h$-expansive action of sofic groups is asymptotically $h$-expansive. We show that each expansive…

We study different types of transitive points in CR-dynamical systems (X,G) with closed relations G on compact metric spaces X. We also introduce transitive and dense orbit transitive CR-dynamical systems and discuss their properties and…

Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…

An action of a group $G$ is highly transitive if $G$ acts transitively on $k$-tuples of distinct points for all $k \geq 1$. Many examples of groups with a rich geometric or dynamical action admit highly transitive actions. We prove that if…

For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…

We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…

In this paper we investigate the action of Polish groups (not necessary abelian) on an uncountable Polish spaces. We consider two main situations. First, when the orbits given by group action are small and the second when the family of…

We study periodic points and finitely supported invariant measures for continuous semigroup actions. Introducing suitable notions of periodicity in both topological and measure-theoretical contexts, we analyze the space of invariant Borel…

For a continuous semicascade on a metrizable compact set $\Omega $, we consider the weak$^{*}$ convergence of generalized operator ergodic means in ${\rm End}\, \, C^{*} (\Omega)$. We discuss conditions on the dynamical system under which…