Non-degenerate Liouville tori are KAM stable
Dynamical Systems
2014-12-02 v1
Abstract
In this short note, we prove that a quasi-periodic torus, with a non-resonant frequency (that can be Diophantine or Liouville) and which is invariant by a sufficiently regular Hamiltonian flow, is KAM stable provided it is Kolmogorov non-degenerate. When the Hamiltonian is smooth (respectively Gevrey-smooth, respectively real-analytic), the in-variant tori are smooth (respectively Gevrey-smooth, respectively real-analytic). This answers a question raised in a recent work by Eliasson, Fayad and Krikorian ([EFK]). We also take the opportunity to ask other questions concerning the stability of non-resonant invariant quasi-periodic tori in (analytic or smooth) Hamiltonian systems.
Keywords
Cite
@article{arxiv.1412.0509,
title = {Non-degenerate Liouville tori are KAM stable},
author = {Abed Bounemoura},
journal= {arXiv preprint arXiv:1412.0509},
year = {2014}
}