Moser's twist theorem revisited
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866911429107384320 |
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| author | Liu, Yi Wang, Lin |
| author_facet | Liu, Yi Wang, Lin |
| contents | Inspired by the work of Katznelson and Ornstein, we present a short way to achieve the almost optimal regularity in Moser's twist theorem. Specifically, for an integrable area-preserving twist map, the invariant circle with a given constant type frequency $α$ persists under a small perturbation (dependent on $α$) of class $C^{3+ε}$. This result was initially established independently by Herman and Rüssmann in 1983. Our method differs essentially from their approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moser's twist theorem revisited Liu, Yi Wang, Lin Dynamical Systems Inspired by the work of Katznelson and Ornstein, we present a short way to achieve the almost optimal regularity in Moser's twist theorem. Specifically, for an integrable area-preserving twist map, the invariant circle with a given constant type frequency $α$ persists under a small perturbation (dependent on $α$) of class $C^{3+ε}$. This result was initially established independently by Herman and Rüssmann in 1983. Our method differs essentially from their approaches. |
| title | Moser's twist theorem revisited |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2502.10969 |