KAM via Standard Fixed Point Theorems

Thomas Alazard; Chengyang Shao

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arXiv · 2312.13971

KAM via Standard Fixed Point Theorems

Thomas Alazard·Chengyang Shao

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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.

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Thomas Alazard, Chengyang Shao. 2023-12-21. KAM via Standard Fixed Point Theorems. https://arxiv.org/abs/2312.13971

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