An entropy dichotomy for singular star flows
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- by Maria José Pacifico, Fan Yang and Jiagang Yang;
- Trans. Amer. Math. Soc. 376 (2023), 6845-6871
- DOI: https://doi.org/10.1090/tran/8989
- Published electronically: July 20, 2023
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Abstract:
We show that non-trivial chain recurrent classes for generic $C^1$ 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 measure. As a result, we show that $C^1$ generic star flows have only finitely many Lyapunov stable chain recurrent classes.References
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Bibliographic Information
- Maria José Pacifico
- Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970 Rio de Janeiro, RJ, Brazil
- MR Author ID: 196844
- ORCID: 0000-0002-7677-5668
- Email: pacifico@im.ufrj.br
- Fan Yang
- Affiliation: Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina
- ORCID: 0000-0002-4954-9681
- Email: yangf@wfu.edu; fizbanyang@gmail.com
- Jiagang Yang
- Affiliation: Department of Mathematics, Southern University of Science and Technology of China, Guangdong, China; and Departamento de Geometria, Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Brazil
- MR Author ID: 949931
- Email: yangjg@impa.br
- Received by editor(s): February 23, 2021
- Received by editor(s) in revised form: July 7, 2022
- Published electronically: July 20, 2023
- Additional Notes: This research had been supported [in part] by CAPES – Finance Code 001 and CNPq-grants. The first author was partially supported by FAPERJ CNE-239069. The third author was partially supported by NSFC 11871487 of China.
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 6845-6871
- MSC (2020): Primary 28D20, 37D45; Secondary 37C10
- DOI: https://doi.org/10.1090/tran/8989
- MathSciNet review: 4636679