Expansive Minimal Flows
Dynamical Systems
2025-08-22 v2
Abstract
In this paper, we extend a Ma\~n\'e's famous result on expansive homeomorphisms, originally presented in [17], to the setting of flows. Specifically, we provide a complete characterization of minimal expansive flows without fixed points on compact metric spaces. We prove that such flows must be defined on one-dimensional sets and are equivalent to the suspension of a minimal subshift. This result significantly improves upon [16] by eliminating the need for their additional hypothesis. Furthermore, we apply our findings to show that any regular expansive flow on a compact metric space of dimension two or higher must contain infinitely many minimal subsets.
Cite
@article{arxiv.2502.10759,
title = {Expansive Minimal Flows},
author = {Alfonso Artigue and Elias Rego},
journal= {arXiv preprint arXiv:2502.10759},
year = {2025}
}
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16 Pages