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arXiv · 2210.12038

Contributions to the Theory of Asymptotically Sectional Hyperbolic Flows

Alexander Arbieto·Miguel Pineda·Elias Rego·Kendry J. Vivas
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Abstract

In this paper, we make several contributions to the theory of asymptotically sectional-hyperbolic (ASH) flows. First, we prove that every star ASH attractor for a $C^2$ vector field is, in fact, sectional-hyperbolic (SH). Second, we establish that all ASH attractors exhibit the property of entropy flexibility. Additionally, we show that any ASH attractor for three-dimensional vector fields is entropy-expansive and admits periodic orbits. Finally, we provide a lower bound for the growth rate of periodic orbits in an ASH attractor.

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Alexander Arbieto, Miguel Pineda, Elias Rego, Kendry J. Vivas. 2022-10-21. Contributions to the Theory of Asymptotically Sectional Hyperbolic Flows. https://arxiv.org/abs/2210.12038

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