Some Properties of Recurrent Sets for Endomorphisms of Topological Groups
General Topology
2019-12-19 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1912.08419,
title = {Some Properties of Recurrent Sets for Endomorphisms of Topological Groups},
author = {Seyyed Alireza Ahmadi and Javad Jamalzadeh and Xinxing Wu},
journal= {arXiv preprint arXiv:1912.08419},
year = {2019}
}
Comments
12 pages