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KAM via Standard Fixed Point Theorems

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arxiv 2312.13971 v3 pith:HJNGKAL3 submitted 2023-12-21 math.AP math.DS

Thomas Alazard , Chengyang Shao This is my paper · ORCID
classification math.APmath.DS
keywords equationsfixedpointstandardargumentconjugacyconverteddiscovery
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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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  1. Finite codimension stability of invariant surfaces

    math.DS 2025-02 conditional novelty 7.0 of 10

    For almost every direction on a translation surface, the invariant surface of the flat geodesic flow persists within a finite-codimension family of smooth Hamiltonian perturbations.

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