Moser's twist theorem revisited

2025/02/16 by Liu, Yi, Wang, Lin
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.10969

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 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.

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