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An Infinite-dimensional KAM Theorem with Normal Degeneracy

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arxiv 2304.06995 v1 pith:LIWWDYRU submitted 2023-04-14 math.DS

Jiayin Du , Lu Xu , Yong Li This is my paper · ORCID
classification math.DS
keywords normaldegeneracyconditionformperturbationanalyticityassumecertain
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In this paper, we consider a classical Hamiltonian normal form with degeneracy in normal direction. In previous results, one needs to assume that the perturbation satisfies certain non-degenerate conditions in order to remove the degeneracy in the normal form. In stead of that, we introduce a topological degree condition and a weak convexity condition, which are easy to be verified, and we prove the persistence of lower dimensional tori without any restriction on perturbation but only smallness and analyticity.

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  1. Measures and Trajectory Properties in Oscillator Systems

    math.DS 2025-06 conditional novelty 6.0 of 10

    Countable oscillator systems are non-wandering, continuous systems with absolutely continuous measures are wandering, and a Fourier condition extends wandering to a class of singular Bernoulli measures.

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