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arXiv · 2608.02186

Komuro Expansivity and Periodic Orbit Growth for Multi-Singular Hyperbolic Flows

Maria José Pacifico·Fan Yang·Jiagang Yang·Rusong Zheng
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Abstract

In this paper we prove that every multi-singular hyperbolic set of a $C^1$ flow is Komuro expansive. This is the strongest natural form of expansivity for flows with singularities accumulated by regular orbits, allowing arbitrary orientation-preserving time reparametrizations. We then use this to establish a two-sided asymptotic counting bound of the form $e^{ht}/t$ for periodic orbits, and prove that the normalized orbit measures converge to the unique measure of maximal entropy. We also establish the same results for a $C^1$ open and dense subset of star vector fields.

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Maria José Pacifico, Fan Yang, Jiagang Yang, Rusong Zheng. 2026-08-03. Komuro Expansivity and Periodic Orbit Growth for Multi-Singular Hyperbolic Flows. https://arxiv.org/abs/2608.02186

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