Moser's twist theorem revisited

Yi Liu; Lin Wang

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arXiv · 2502.10969

Moser's twist theorem revisited

Yi Liu·Lin Wang

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Abstract

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 $\alpha$ persists under a small perturbation (dependent on $\alpha$) of class $C^{3+\epsilon}$. This result was initially established independently by Herman and R\"{u}ssmann in 1983. Our method differs essentially from their approaches.

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Yi Liu, Lin Wang. 2025-02-16. Moser's twist theorem revisited. https://arxiv.org/abs/2502.10969

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