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

Seyyed Alireza Ahmadi

Iran, Islamic Republic of

University of Sistan and Baluchestan

Submitted: 2014-06-05

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Accepted: 2014-06-05

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Published: 2014-06-12

DOI: https://doi.org/10.4995/agt.2014.3050
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Keywords:

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

Supporting agencies:

This research was not funded

Abstract:

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.
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