First-time sensitive homeomorphisms

Fuente: arXiv
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Autores principales: Antunes, Mayara, Carvalho, Bernardo
Formato: Preprint
Publicado: 2023
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author Antunes, Mayara
Carvalho, Bernardo
author_facet Antunes, Mayara
Carvalho, Bernardo
contents We introduce first-time sensitivity for a homeomorphism of a compact metric space, that is a condition on the first increasing times of open balls of the space. Continuum-wise expansive homeomorphisms, the shift map on the Hilbert cube, and also some partially hyperbolic diffeomorphisms satisfy this condition. We prove the existence of local unstable continua satisfying similar properties with the local unstable continua of cw-expansive homeomorphisms, but assuming first-time sensitivity. As a consequence we prove that first-time sensitivity (with some additional technical assumptions) implies positive topological entropy.
format Preprint
id arxiv_https___arxiv_org_abs_2304_03123
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle First-time sensitive homeomorphisms
Antunes, Mayara
Carvalho, Bernardo
Dynamical Systems
We introduce first-time sensitivity for a homeomorphism of a compact metric space, that is a condition on the first increasing times of open balls of the space. Continuum-wise expansive homeomorphisms, the shift map on the Hilbert cube, and also some partially hyperbolic diffeomorphisms satisfy this condition. We prove the existence of local unstable continua satisfying similar properties with the local unstable continua of cw-expansive homeomorphisms, but assuming first-time sensitivity. As a consequence we prove that first-time sensitivity (with some additional technical assumptions) implies positive topological entropy.
title First-time sensitive homeomorphisms
topic Dynamical Systems
url https://arxiv.org/abs/2304.03123