{"title":"A topological characterization of periodic flows","authors":"Khadija Ben Rejeb","doi":"10.1080/14689367.2022.2130033","DOIUrl":null,"url":null,"abstract":"Let be a continuous flow of homeomorphisms of a connected n-manifold M. The flow G is called periodic if: for some real s>0, . A global section for a flow G is a closed subset K of M such that every orbit under G intersects K in exactly one point. In this paper, we give a topological characterization of periodic flows with global sections for . Next, we consider periodic flows defined on any connected n-manifold M, and we give a similar local characterization.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"38 1","pages":"20 - 29"},"PeriodicalIF":0.5000,"publicationDate":"2022-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2022.2130033","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Let be a continuous flow of homeomorphisms of a connected n-manifold M. The flow G is called periodic if: for some real s>0, . A global section for a flow G is a closed subset K of M such that every orbit under G intersects K in exactly one point. In this paper, we give a topological characterization of periodic flows with global sections for . Next, we consider periodic flows defined on any connected n-manifold M, and we give a similar local characterization.
期刊介绍：
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences
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