On the topology of the chain recurrent set of a dynamical system

Seyyed Alireza Ahmadi


n this paper we associate a pseudo-metric to a dynamical system on a compact metric space. We show that this pseudo-metric is identically zero if and only if the system is chain transitive. If we associate this pseudo-metric to the identity map, then we can present a  characterization for connected and totally disconnected metric spaces.


chain recurrent; chain transitive; chain component; inverse limit space.

Subject classification

337B35; 54H20.

Full Text:



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1. Topological chain and shadowing properties of dynamical systems on uniform spaces
Seyyed Alireza Ahmadi, Xinxing Wu, Guanrong Chen
Topology and its Applications  vol: 275  first page: 107153  year: 2020  
doi: 10.1016/j.topol.2020.107153

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt