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Nonchaotic N-expansive homeomorphisms

Part of: Topological dynamics Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  31 August 2023

Woochul Jung  and
C. A. Morales
Woochul Jung
Affiliation:
Healthcare Data Science Center, Konyang University Hospital, Daejeon, Republic of Korea (wcjungdynamics@gmail.com)
C. A. Morales
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil (morales@impa.br)
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Abstract

In this paper, we give necessary conditions for an $N$-expansive homeomorphism of a compact metric space to be nonchaotic in the Li–Yorke sense. As application we give a partial answer to a conjecture in [2].

Keywords

compact metric spaceexpansiveN-expansive

MSC classification

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Secondary: 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 9
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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