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Transactions of the American Mathematical Society

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Flows without wandering points on compact connected surfaces


Authors: Milton Cobo, Carlos Gutierrez and Jaume Llibre
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
Published electronically: April 14, 2010
MathSciNet review: 2645042
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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$.


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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
Email: jllibre@mat.uab.cat

DOI: https://doi.org/10.1090/S0002-9947-10-05113-5
Keywords: Interval exchange transformation, flows in compact surfaces, wandering sets
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.
Article copyright: © Copyright 2010 American Mathematical Society

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