Lyapunov stable chain recurrence classes for singular flows
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916488734048256 |
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| author | Gan, Shaobo Yang, Jiagang Zheng, Rusong |
| author_facet | Gan, Shaobo Yang, Jiagang Zheng, Rusong |
| contents | We show that for a $C^1$ generic vector field $X$ away from homoclinic tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic class. The proof uses an argument with $C^2$ vector fields approaching $X$ in $C^1$ topology, with their Gibbs $F$-states converging to a Gibbs $F$-state of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_09742 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lyapunov stable chain recurrence classes for singular flows Gan, Shaobo Yang, Jiagang Zheng, Rusong Dynamical Systems 37C10, 37C27, 37C29, 37D30 We show that for a $C^1$ generic vector field $X$ away from homoclinic tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic class. The proof uses an argument with $C^2$ vector fields approaching $X$ in $C^1$ topology, with their Gibbs $F$-states converging to a Gibbs $F$-state of $X$. |
| title | Lyapunov stable chain recurrence classes for singular flows |
| topic | Dynamical Systems 37C10, 37C27, 37C29, 37D30 |
| url | https://arxiv.org/abs/2202.09742 |