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arXiv · 2609.00626

Entropy on regular sets and periodic-orbit growth for singular flows

C. A. Morales
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Abstract

We study entropy and periodic-orbit growth for flows on metric spaces. First, we prove that the finite topological entropy of a flow on a compact metric space is completely carried by compact subsets of its regular set. Next, we establish a Bowen--Walters inequality for geometrically separating flows on possibly noncompact metric spaces, under uniform control at time zero and dynamical isolation at infinity. As applications, we obtain the Bowen--Walters inequality for singular suspension flows over expansive homeomorphisms, multisingular-hyperbolic sets---extending the upper-bound part of \cite{pyyz}---and asymptotically sectional-hyperbolic attractors such as Rovella's \cite{r}.

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C. A. Morales. 2026-09-01. Entropy on regular sets and periodic-orbit growth for singular flows. https://arxiv.org/abs/2609.00626

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