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

2026/08/03 by Maria José Pacifico, Fan Yang, Jiagang Yang +1
Mathematics · #math.DS #msc:37D05 #msc:37C27 #msc:37C35 #msc:37C40 #msc:37C70

paper · pdf

49 pages and 3 figures

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

In this paper we prove that every multi-singular hyperbolic set of a C¹ 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 C¹ open and dense subset of star vector fields.

Citations

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