arXiv subjects

C. Uzcátegui

Publications and source records attributed to C. Uzcátegui.

4 recordsLinked to original sources

arXiv2019

On the continuity of the elements of the Ellis semigroup and other properties

We consider discrete dynamical systems whose phase spaces are compact metrizable countable spaces. In the first part of the article, we study some properties that guarantee the continuity of all functions of the corresponding Ellis semigroup. For instance, if every accumulation point of $X$ is fixed, we give a necessary and sufficient condition on a point $a\in X'$ in order that all functions of the Ellis semigroup $E(X,f)$ be continuous at the given point $a$. In the second part, we consider transitive dynamical systems. We show that if $(X,f)$ is a transitive dynamical system and either every function of $E(X,f)$ is continuous or $|ω_f(x)|=1$ for each accumulation point $x$ of $X$, then $E(X,f)$ is homeomorphic to $X$. Several examples are given to illustrate our results.

math.GN↗

arXiv2017

On the continuity of partial actions of Hausdorff groups on metric spaces

We provide a sufficient condition for a topological partial action of a Hausdorff group on a metric space is continuous, provide that it is separately continuous.

math.DS↗

arXiv2017

The open mapping principle for partial actions of polish groups

We present a extension of the classical open mapping principle and Effros' theorem for Polish group actions to the context of partial group actions.

math.FA↗

arXiv2016

Iterates of dynamical systems on compact metrizable countable spaces

Given a dynamical system $(X,f)$, we let $E(X,f)$ denote its Ellis semigroup and $E(X,f)^* = E(X,f) \setminus \{f^n : n \in \mathbb{N}\}$. We analyze the Ellis semigroup of a dynamical system having a compact metric countable space as a phase space. We show that if $(X,f)$ is a dynamical system such that $X$ is a compact metric countable space and every accumulation point $X'$ is periodic, then either each function of $E(X,f)^*$ is continuous or each function of $E(X,f)^*$ is discontinuous. We describe an example of a dynamical system $(X,f)$ where $X$ is a compact metric countable space, the orbit of each accumulation point is finite and $E(X,f)^*$ contains continuous and discontinuous functions.

math.GN↗