非准周期正态理论

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2023-12-07 DOI:10.1134/S1560354723060035

Gabriella Pinzari

{"title":"非准周期正态理论","authors":"Gabriella Pinzari","doi":"10.1134/S1560354723060035","DOIUrl":null,"url":null,"abstract":"<div><p>We review a recent application of the ideas of normal form theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference\nfrom the standard case consists in the non-uniqueness of the normal form and the total absence of the small\ndivisors problem. The exposition is quite general, so as to allow extensions to the case\nof more non-periodic coordinates, and more functional settings. Here, for simplicity,\nwe work in the real-analytic class.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 6","pages":"841 - 864"},"PeriodicalIF":0.8000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Quasi-Periodic Normal Form Theory\",\"authors\":\"Gabriella Pinzari\",\"doi\":\"10.1134/S1560354723060035\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We review a recent application of the ideas of normal form theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference\\nfrom the standard case consists in the non-uniqueness of the normal form and the total absence of the small\\ndivisors problem. The exposition is quite general, so as to allow extensions to the case\\nof more non-periodic coordinates, and more functional settings. Here, for simplicity,\\nwe work in the real-analytic class.</p></div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"28 6\",\"pages\":\"841 - 864\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-12-07\",\"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/S1560354723060035\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354723060035","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

摘要

我们回顾了最近将正则表达式理论的思想应用于扰动项在一个坐标变量中不是周期性的系统（汉密尔顿系统或一般 ODE）的情况。与标准情况的主要区别在于正则表达式的非唯一性和完全不存在小二维问题。本文的论述非常宽泛，可以扩展到更多非周期坐标和更多函数设置的情况。在此，为简单起见，我们在实解析类中进行研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Non-Quasi-Periodic Normal Form Theory

We review a recent application of the ideas of normal form theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference from the standard case consists in the non-uniqueness of the normal form and the total absence of the small divisors problem. The exposition is quite general, so as to allow extensions to the case of more non-periodic coordinates, and more functional settings. Here, for simplicity, we work in the real-analytic class.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.