Rescaled-Expansive Flows: Unstable Sets and Topological Entropy
Dynamical Systems
2025-08-22 v3
Abstract
In this work we introduce and explore a rescaled-theory of local stable and unstable sets for rescaled-expansive flows and its applications to topological entropy. We introduce a rescaled version of the local unstable sets and the unstable points. We find conditions for points of the phase space to exhibit non-trivial connected pieces of such unstable sets. We apply these results to the problem of proving positive topological entropy for rescaled-expansive flows with non-singular Lyapunov stable sets.
Cite
@article{arxiv.2107.01708,
title = {Rescaled-Expansive Flows: Unstable Sets and Topological Entropy},
author = {Alexander Arbieto and Alfonso Artigue and Elias Rego},
journal= {arXiv preprint arXiv:2107.01708},
year = {2025}
}