Flows without wandering points on compact connected surfaces

Cobo, Milton; Gutierrez, Carlos; Llibre, Jaume

doi:10.1090/S0002-9947-10-05113-5

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 $\varphi$.

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