An entropy dichotomy for singular star flows
Dynamical Systems
2021-01-26 v1
Abstract
We show that non-trivial chain recurrent classes for generic star flows satisfy a dichotomy: either they have zero topological entropy, or they must be isolated. Moreover, chain recurrent classes for generic star flows with zero entropy must be sectional hyperbolic, and cannot be detected by any non-trivial ergodic invariant probability. As a result, we show that generic star flows have only finitely many Lyapunov stable chain recurrent classes.
Keywords
Cite
@article{arxiv.2101.09480,
title = {An entropy dichotomy for singular star flows},
author = {Maria José Pacifico and Fan Yang and Jiagang Yang},
journal= {arXiv preprint arXiv:2101.09480},
year = {2021}
}
Comments
24 pages, 4 figures. arXiv admin note: text overlap with arXiv:1901.07436