{"title":"Topology of horocycles on geometrically finite nonpositively curved surfaces","authors":"Sergi Burniol Clotet","doi":"10.1007/s10711-024-00941-z","DOIUrl":null,"url":null,"abstract":"<p>We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10711-024-00941-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow.