An Infinite-dimensional KAM Theorem with Normal Degeneracy
Dynamical Systems
2024-05-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2304.06995,
title = {An Infinite-dimensional KAM Theorem with Normal Degeneracy},
author = {Jiayin Du and Lu Xu and Yong Li},
journal= {arXiv preprint arXiv:2304.06995},
year = {2024}
}