Singular KAM Theory for Convex Hamiltonian Systems

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-08-11 DOI:10.1134/S1560354725040057

Santiago Barbieri, Luca Biasco, Luigi Chierchia, Davide Zaccaria

引用次数: 0

Abstract

In this note, we briefly discuss how the singular KAM theory of [7] — which was worked out for the mechanical case \(\frac{1}{2}|y|^{2}+\varepsilon f(x)\) — can be extended to convex real-analytic nearly integrable Hamiltonian systems with Hamiltonian in action-angle variables given by \(h(y)+\varepsilon f(x)\) with \(h\) convex and \(f\) generic.

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凸哈密顿系统的奇异KAM理论

在这篇笔记中，我们简要地讨论了如何将[7]的奇异KAM理论——它是在机械情况\(\frac{1}{2}|y|^{2}+\varepsilon f(x)\)下得到的——推广到具有作用角变量的哈密顿量的凸实-解析近可积哈密顿系统中，该哈密顿量由\(h(y)+\varepsilon f(x)\)给出，具有\(h\)凸和\(f\)一般。

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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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.