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- Title
RECURRENT SETS FOR ENDOMORPHISMS OF TOPOLOGICAL GROUPS.
- Authors
AHMADI, SEYYED ALIREZA; JAMALZADEH, JAVAD
- 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, we show that some dynamical properties are induced by the original system on quotient spaces. These results link an algebraic property to a dynamical property.
- Subjects
TOPOLOGICAL groups; ENDOMORPHISMS; METRIC spaces; TOPOLOGICAL entropy
- Publication
Mathematica (1222-9016), 2024, Vol 66, Issue 1, p18
- ISSN
1222-9016
- Publication type
Article
- DOI
10.24193/mathcluj.2024.1.02