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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.

Keywords

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

R2 v1 2026-06-28T13:58:51.931Z