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arXiv · 2107.01708

Rescaled-Expansive Flows: Unstable Sets and Topological Entropy

Alexander Arbieto·Alfonso Artigue·Elias Rego
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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.

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Alexander Arbieto, Alfonso Artigue, Elias Rego. 2021-07-04. Rescaled-Expansive Flows: Unstable Sets and Topological Entropy. https://doi.org/10.12775/tmna.2024.024

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