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arXiv · 2304.03123

First-time sensitive homeomorphisms

Mayara Antunes·Bernardo Carvalho
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Abstract

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.

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Mayara Antunes, Bernardo Carvalho. 2023-04-06. First-time sensitive homeomorphisms. https://doi.org/10.1007/s10884-024-10362-x

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