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Some Properties of Recurrent Sets for Endomorphisms of Topological Groups

2019/12/18 by Seyyed Alireza Ahmadi, Ahmadi, Seyyed Alireza, Javad Jamalzadeh +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1912.08419

openalex publication_date 2019/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent points and chain transitive component of the identity are topological subgroups. Furthermore, it is obtained that some dynamical properties induced by the original system on quotient spaces. These results link an algebraic property to a dynamical property.

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