Nineteen Fifty-Four: Kolmogorov’s New “Metrical Approach” to Hamiltonian Dynamics

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2024-07-05 DOI:10.1134/S1560354724550021

Luigi Chierchia, Isabella Fascitiello

引用次数: 0

Abstract

We review Kolmogorov’s 1954 fundamental paper On the persistence of conditionally periodic motions under a small change in the Hamilton function (Dokl. akad. nauk SSSR, 1954, vol. 98, pp. 527–530), both from the historical and the mathematical point of view. In particular, we discuss Theorem 2 (which deals with the measure in phase space of persistent tori), the proof of which is not discussed at all by Kolmogorov, notwithstanding its centrality in his program in classical mechanics.

In Appendix, an interview (May 28, 2021) to Ya. Sinai on Kolmogorov’s legacy in classical mechanics is reported.

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19 54：科尔莫戈罗夫的汉密尔顿动力学新 "韵律方法

我们从历史和数学的角度回顾了科尔莫戈罗夫 1954 年的基本论文《论汉密尔顿函数微小变化下条件周期运动的持久性》（《苏联科学院学报》，1954 年，第 98 卷，第 527-530 页）。我们特别讨论了定理 2（涉及持久环的相空间度量），尽管该定理在科尔莫戈罗夫的经典力学计划中占据核心地位，但科尔莫戈罗夫根本没有讨论过该定理的证明。西奈的访谈（2021 年 5 月 28 日）。

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.