{"title":"Nineteen Fifty-Four: Kolmogorov’s New “Metrical Approach” to Hamiltonian Dynamics","authors":"Luigi Chierchia, Isabella Fascitiello","doi":"10.1134/S1560354724550021","DOIUrl":null,"url":null,"abstract":"<div><p>We review Kolmogorov’s 1954 fundamental paper <i>On the persistence of conditionally periodic motions under a small change in the Hamilton function</i> (Dokl. akad. nauk SSSR, 1954, vol. <b>98</b>, pp. 527–530), both from the historical and the mathematical point of view.\nIn 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.</p><p>In Appendix, an interview (May 28, 2021) to Ya. Sinai on Kolmogorov’s legacy in classical mechanics is reported.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 and Dmitry Treschev)","pages":"517 - 535"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354724550021","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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