Some remarks on the optimality of the Bruno-R{\"u}ssmann condition
Dynamical Systems
2018-01-11 v1
Abstract
We prove that the Bruno-R{\"u}ssmann condition is optimal for the analytic preservation of a quasi-periodic invariant curve for an analytic twist map. The proof is based on Yoccoz's corresponding result for analytic circle diffeomorphisms and the uniqueness of invariant curves with a given irrational rotation number. We also prove a similar result for analytic Tonelli Hamiltonian flow with n = 2 degrees of freedom; for n 3 we only obtain a weaker result which recovers and slightly improves a theorem of Bessi.
Keywords
Cite
@article{arxiv.1801.03343,
title = {Some remarks on the optimality of the Bruno-R{\"u}ssmann condition},
author = {Abed Bounemoura},
journal= {arXiv preprint arXiv:1801.03343},
year = {2018}
}