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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.01009 |
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Table of 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.