{"title":"$$\\mathbb {Z}$ -扩展中自相交轨迹的极限定理","authors":"Maxence Phalempin","doi":"10.1007/s00220-024-04972-1","DOIUrl":null,"url":null,"abstract":"<p>We investigate the asymptotic properties of the self-intersection numbers for <span>\\(\\mathbb {Z}\\)</span>-extensions of chaotic dynamical systems, including the <span>\\(\\mathbb {Z}\\)</span>-periodic Lorentz gas and the geodesic flow on a <span>\\(\\mathbb {Z}\\)</span>-cover of a negatively curved compact surface. We establish a functional limit theorem.\n</p>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Limit Theorems for Self-Intersecting Trajectories in $$\\\\mathbb {Z}$$ -Extensions\",\"authors\":\"Maxence Phalempin\",\"doi\":\"10.1007/s00220-024-04972-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We investigate the asymptotic properties of the self-intersection numbers for <span>\\\\(\\\\mathbb {Z}\\\\)</span>-extensions of chaotic dynamical systems, including the <span>\\\\(\\\\mathbb {Z}\\\\)</span>-periodic Lorentz gas and the geodesic flow on a <span>\\\\(\\\\mathbb {Z}\\\\)</span>-cover of a negatively curved compact surface. We establish a functional limit theorem.\\n</p>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s00220-024-04972-1\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s00220-024-04972-1","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了混沌动力系统的(\(\mathbb {Z}\)-extensions of chaotic dynamical systems)自交数的渐近性质,包括(\(\mathbb {Z}\)-periodic Lorentz gas)周期洛伦兹气体和(\(\mathbb {Z}\)-cover of a negatively curved compact surface)负弯曲紧凑曲面上的大地流。我们建立了一个函数极限定理。
Limit Theorems for Self-Intersecting Trajectories in $$\mathbb {Z}$$ -Extensions
We investigate the asymptotic properties of the self-intersection numbers for \(\mathbb {Z}\)-extensions of chaotic dynamical systems, including the \(\mathbb {Z}\)-periodic Lorentz gas and the geodesic flow on a \(\mathbb {Z}\)-cover of a negatively curved compact surface. We establish a functional limit theorem.
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.