Moser's twist theorem revisited
Abstract
Inspired by the work of Katznelson and Ornstein [10], 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+\varepsilon} $. This result was initially established independently by Herman [7] and Rüssmann [18] in 1983. Our method differs essentially from their approaches.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 51
- Issue
- 0
- Pages
- 514–541
- Publication date
- 1 January 2026
- Language
- EN