On the accumulation of separatrices by invariant circles
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866908625009639424 |
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| author | Katok, Anatole Krikorian, Raphaël |
| author_facet | Katok, Anatole Krikorian, Raphaël |
| contents | Let $f$ be a smooth symplectic diffeomorphism of $\mathbb{R}^2$ admitting a (non-split) separatrix associated to a hyperbolic fixed point. We prove that if $f$ is a perturbation of the time-1 map of a symplectic autonomous vector field, this separatrix is accumulated by a positive measure set of invariant circles. On the other hand, we provide examples of smooth symplectic diffeomorphisms with a Lyapunov unstable non-split separatrix that are not accumulated by invariant circles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_10137 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the accumulation of separatrices by invariant circles Katok, Anatole Krikorian, Raphaël Dynamical Systems 37J Let $f$ be a smooth symplectic diffeomorphism of $\mathbb{R}^2$ admitting a (non-split) separatrix associated to a hyperbolic fixed point. We prove that if $f$ is a perturbation of the time-1 map of a symplectic autonomous vector field, this separatrix is accumulated by a positive measure set of invariant circles. On the other hand, we provide examples of smooth symplectic diffeomorphisms with a Lyapunov unstable non-split separatrix that are not accumulated by invariant circles. |
| title | On the accumulation of separatrices by invariant circles |
| topic | Dynamical Systems 37J |
| url | https://arxiv.org/abs/2109.10137 |