Related papers: Limit Sets and Internal Transitivity in Free Group…
It is well known that \omega-limit sets are internally chain transitive and have weak incompressibility; the converse is not generally true, in either case. However, it has been shown that a set is weakly incompressible if and only if it is…
Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…
We consider which spaces can be realized as the omega limit set of the discrete time dynamical system. This is equivalent to asking which spaces admit a chain transitive homeomorphism and which do not. This leads us to ask for spaces where…
In this paper we consider the structure of $\omega$-limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate that many classical structure theorems for $\omega$-limit…
This paper examines the relationship between shadowing phenomena and the continuity properties of $\omega$-limit sets in dynamical systems. We give a necessary and sufficient condition for a shadowable point to be an upper (resp. a lower)…
For a continuous map f on a compact metric space (X,d), a subset D of X is internally chain transitive if for every x and y in D and every delta > 0 there is a sequence of points {x=x_0,x_1, ...,x_n=y} such that d(f(x_i),x_{i+1}) < delta…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
Asymptotic properties of discrete, stochastic approximations to hybrid systems, modeled as hybrid inclusions, are studied. First, the internal chain transitivity of omega-limits of solutions is concluded, along with other properties related…
We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…
We wish to investigate some elementary problems concerning topological dynamics revolving around our proposed definition of escaping set. We also discuss the notion of escaping set in the induced dynamics of the hyperspace. Moreover, we…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
In this paper we study the action of semigroups with nonempty interior of noncompact connected semisimple Lie groups, with finite center, on their maximal compact connected subgroups. As main results we describe the set of transitivity of a…
Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…
This note is a brief review of the analysis of long transients in dynamical systems. The problem of long transients arose in many disciplines, from physical and chemical kinetic to biology and even social sciences. Detailed analysis of…
We examine certain phenomena in $C^1$-dynamics from a viewpoint of shadowing and improve a known result on hyperbolic sets. We also review a result on the stability of attractor boundaries from the same viewpoint and derive several…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical…
We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different…
We study the interplay between the algebraic and dynamical properties of groups that admit a general type action on a $\delta$-hyperbolic space such that the induced action on the limit set of the Gromov boundary is faithful. We divide the…
In this article, we deal with several notions in dynamical systems. Firstly, we prove that both closure function and orbital function are idempotent on set-valued dynamical systems. And we show that the compact limit set of a connected set…