{"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}
引用次数: 0
Abstract
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.