English

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.

Keywords

Cite

@article{arxiv.2502.10759,
  title  = {Expansive Minimal Flows},
  author = {Alfonso Artigue and Elias Rego},
  journal= {arXiv preprint arXiv:2502.10759},
  year   = {2025}
}

Comments

16 Pages

R2 v1 2026-06-28T21:45:24.171Z