退化拟周期可逆映射不变曲线的存在性

Pub Date : 2022-01-01 DOI:10.11650/tjm/220201

Peng-Ruei Huang

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摘要

本文研究了在Brjuno–Rüssmann非共振条件下，具有扭曲条件的高阶退化的拟周期可逆映射的不变曲线的存在性。在证明中，我们使用了KAM理论的一个新变体，包含一个人工参数q，0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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Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings

In this paper we are concerned with the existence of invariant curves of quasi-periodic reversible mappings with higher order degeneracy of the twist condition under the Brjuno–Rüssmann’s non-resonant condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter q, 0 < q < 1, which makes the steps of the KAM iteration infinitely small in the speed of function qε, rather than super exponential function.