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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{morales2026entropy,
  title = {{Entropy on regular sets and periodic-orbit growth for singular flows}},
  author = {C. A. Morales},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00626},
  eprint = {2609.00626},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00626},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Entropy on regular sets and periodic-orbit growth for singular flows
AU  - C. A. Morales
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00626
UR  - https://arxiv.org/abs/2609.00626
AB  - 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}.
ER  -