Proof of the $C^2$ Mañé's conjecture on surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916344189943808 |
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| author | Contreras, Gonzalo |
| author_facet | Contreras, Gonzalo |
| contents | We prove that $C^2$ generic hyperbolic Mañé sets contain a periodic periodic orbit. In dimension 2, adding a result by Contreras, Figalli, Rifford, which states that $C^2$ generic Mañé sets are hyperbolic; we obtain Mañé's Conjecture for surfaces in the $C^2$ topology: Given a Tonelli Lagrangian $L$ on a compact surface $M$ there is a $C^2$ open and dense set of functions $f:M\to\mathbb{R}$ such that the Mañé set of the Lagrangian $L+f$ is a hyperbolic periodic orbit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proof of the $C^2$ Mañé's conjecture on surfaces Contreras, Gonzalo Dynamical Systems We prove that $C^2$ generic hyperbolic Mañé sets contain a periodic periodic orbit. In dimension 2, adding a result by Contreras, Figalli, Rifford, which states that $C^2$ generic Mañé sets are hyperbolic; we obtain Mañé's Conjecture for surfaces in the $C^2$ topology: Given a Tonelli Lagrangian $L$ on a compact surface $M$ there is a $C^2$ open and dense set of functions $f:M\to\mathbb{R}$ such that the Mañé set of the Lagrangian $L+f$ is a hyperbolic periodic orbit. |
| title | Proof of the $C^2$ Mañé's conjecture on surfaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2408.01009 |