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November  2021, 41(11): 5165-5182. doi: 10.3934/dcds.2021072

Uniqueness properties of the KAM curve

 IMJ-PRG, Université de Paris, Paris, France

Received  April 2020 Revised  March 2021 Published  November 2021 Early access  April 2021

Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. When seen as a function of the frequency this invariant collection of tori is called the KAM curve of the system. Restricted to analytic regularity, we obtain strong uniqueness properties for these objects. In particular, we prove that KAM curves completely characterize the underlying systems. We also show some of the dynamical implications on systems whose KAM curves share certain common features.

Citation: Frank Trujillo. Uniqueness properties of the KAM curve. Discrete & Continuous Dynamical Systems, 2021, 41 (11) : 5165-5182. doi: 10.3934/dcds.2021072
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