PreprintCC BY 4.0arXiv
At most exponential growth of periodic orbits for star flows
Abstract
We prove that on any closed manifold there exists a C1 open and dense subset of star flows for which the periodic orbits grow at most expo- nentially. We also explain how our methods apply to the sectional-hyperbolic attractors including the Lorenz polynomial equation.
Related
- Higher-order asymptotic formulae for periodic orbits of 3-dimensional volume-preserving Anosov flows and the Foulon conjecture
- Entropy on regular sets and periodic-orbit growth for singular flows
- Lyapunov-Schmidt reduction for periodic orbits of implicit discrete dynamical systems
- Variational Persistence of Periodic and Quasi-Periodic Orbits in Symmetric N-Body Problems
- Hyperbolic periodic orbits and optimal 1/t convergence of the Lax--Oleinik semigroup
BibTeX
@misc{morales2026most,
title = {{At most exponential growth of periodic orbits for star flows}},
author = {C. A. Morales and E. Rego and X. Wen},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30119},
eprint = {2608.30119},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30119},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - At most exponential growth of periodic orbits for star flows
AU - C. A. Morales
AU - E. Rego
AU - X. Wen
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30119
UR - https://arxiv.org/abs/2608.30119
AB - We prove that on any closed manifold there exists a C1 open and dense subset of star flows for which the periodic orbits grow at most expo- nentially. We also explain how our methods apply to the sectional-hyperbolic attractors including the Lorenz polynomial equation.
ER -