Quasi-analytic properties of the KAM curve
Dynamical Systems
2020-05-19 v2
Abstract
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 quasi-analyticity 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.
Cite
@article{arxiv.1912.13102,
title = {Quasi-analytic properties of the KAM curve},
author = {Frank Trujillo},
journal= {arXiv preprint arXiv:1912.13102},
year = {2020}
}