Work

Nonwandering sets and the entropy of local homeomorphisms

Year: 2025

Type: article

Abstract: Local homeomorphisms between open subsets of a locally compact Hausdorff space induces dynamical systems with a wide range of applications, including in C*-algebras. In this paper, we introduce the concepts of nonwandering and wandering sets for such systems and show that, under mild conditions, the metric entropy is concentrated in the nonwandering set. More generally, we demonstrate that the entropy of the system is the maximum of the entropies of the systems restricted to the nonwandering set and the closure of the wandering set. We illustrate these results with several examples, including applications to subshifts over countable alphabets.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025119

Authors: Daniel Gonçalves, Danilo Royer, Felipe Augusto Tasca

Institutions: Instituto Federal do Paraná, Universidade Federal de Santa Catarina

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina

OpenAlex ID: W4412820016

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Cites: 14

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Related to: 10