Fixed point theorems for small divisors problems
Dynamical Systems
2026-05-12 v2 Functional Analysis
Abstract
In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its applications require, as a general rule, some efforts. We develop further the analytic theory and give fixed point theorems with direct applications to the study of dynamical systems.In practice, our theorems show that Bruno conditions are sufficient to ensure the existence of a positive measure set of invariant tori.
Cite
@article{arxiv.2504.19808,
title = {Fixed point theorems for small divisors problems},
author = {Mauricio Garay and Duco van Straten},
journal= {arXiv preprint arXiv:2504.19808},
year = {2026}
}
Comments
To appear in Functional Analysis and Its Applications