具有正常退化性的无限维 KAM 定理

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-05-14 DOI:10.1088/1361-6544/ad45a1

Jiayin Du, Lu Xu and Yong Li

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引用次数: 0

摘要

在本文中，我们考虑了在法线方向上具有退化性的经典哈密顿法线形式。在以往的结果中，我们需要假设扰动满足某些非退化条件，才能消除法向形式中的退化。与之相反，我们引入了拓扑度条件和弱凸性条件，这两个条件很容易验证，而且我们证明了低维磁环的持久性，对扰动没有任何限制，只有小性和解析性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An infinite dimensional KAM theorem with normal degeneracy

In this paper, we consider a classical Hamiltonian normal form with degeneracy in the 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. Instead of that, we introduce a topological degree condition and a weak convexity condition, which are easy to verify, and we prove the persistence of lower dimensional tori without any restriction on perturbation but only smallness and analyticity.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.