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Approximate Topological Conjugacy

Approximate Topological Conjugacy In this article, we study approximately topological conjugacies for continuous maps on compact metric spaces. It is proven that topological entropy generally is not an invariant for this equivalence. In particular, we discuss the approximately topologically conjugate classifications for circle homeomorphisms, rotations and automorphisms on torus. Mutually topological semi-conjugacy is also studied and compared with approximate topological conjugacy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

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References (21)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2022
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-022-01257-5
Publisher site
See Article on Publisher Site

Abstract

In this article, we study approximately topological conjugacies for continuous maps on compact metric spaces. It is proven that topological entropy generally is not an invariant for this equivalence. In particular, we discuss the approximately topologically conjugate classifications for circle homeomorphisms, rotations and automorphisms on torus. Mutually topological semi-conjugacy is also studied and compared with approximate topological conjugacy.

Journal

Bulletin of the Malaysian Mathematical Sciences SocietySpringer Journals

Published: May 1, 2022

Keywords: Approximate conjugacies; Semi-conjugacies; Circle homeomorphisms; Rotations; Automorphisms; Primary 54H20; Secondary 37E10; 37E45

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