KAM via Standard Fixed Point Theorems
Analysis of PDEs
2025-03-31 v3 Dynamical Systems
Abstract
With a mere usage of well-established properties of para-differential operators, the conjugacy equations in several model KAM problems are converted to para-homological equations solvable by standard fixed point argument. Such discovery greatly simplifies KAM proofs, renders the traditional KAM iteration steps unnecessary, and may suggest a systematic scheme of finding quasi-periodic solutions of realistic magnitude.
Cite
@article{arxiv.2312.13971,
title = {KAM via Standard Fixed Point Theorems},
author = {Thomas Alazard and Chengyang Shao},
journal= {arXiv preprint arXiv:2312.13971},
year = {2025}
}
Comments
Subsection 4.1 corrected