Flows without wandering points on compact connected surfaces
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- by Milton Cobo, Carlos Gutierrez and Jaume Llibre PDF
- Trans. Amer. Math. Soc. 362 (2010), 4569-4580 Request permission
Abstract:
Given a compact $2$–dimensional manifold $M$ we classify all continuous flows $\varphi$ without wandering points on $M$. This classification is performed by finding finitely many pairwise disjoint open $\varphi -$invariant subsets $\{U_1, U_2, \ldots , U_n\}$ of $M$ such that $\bigcup _{i=1}^n{\overline {U_i}} = M$ and each $U_i$ is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of $\varphi$.References
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Additional Information
- Milton Cobo
- Affiliation: Departamento de Matemática, Universidade Federal do Espírito Santo, Av. Fernando Ferrari 514, Vitoria, ES 19075-910 Brazil
- Email: milton.e.cobo@gmail.com
- Carlos Gutierrez
- Affiliation: Departamento de Mateática, Instituto de Ciências Matemáticas e de Computação, Universidade de Sao Paulo, CxP 668, São Carlos, SP, 13560-970 Brazil
- Jaume Llibre
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Catalonia, Spain
- MR Author ID: 115015
- ORCID: 0000-0002-9511-5999
- Email: jllibre@mat.uab.cat
- Received by editor(s): May 10, 2008
- Published electronically: April 14, 2010
- Additional Notes: Unfortunately the second author died during the period that this manuscript was submitted.
- © Copyright 2010 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 362 (2010), 4569-4580
- MSC (2000): Primary 37B05, 37B10, 47B36, 47B37
- DOI: https://doi.org/10.1090/S0002-9947-10-05113-5
- MathSciNet review: 2645042