A structure theorem for foliations on non-compact 2-manifolds

Abstract

Link to this article: http://journals.cambridge.org/abstract_S014338570400029XHow to cite this article: AMÉRICO LÓPEZ (2005). A structure theorem for foliations on non-compact 2-manifolds. Ergodic Theory and Dynamical Systems, 25, pp 893-912Abstract. In this work, singular orientable foliations which admit non-trivial recurrent leaves on 2-manifolds of finite or infinite genus are considered. A structure theorem for such foliations is given. The theorem is similar to Gutierrez's structure theorem (C. Gutierrez. Smoothing continuous flows on 2-manifolds and recurrences. Ergod. Th. & Dynam. Sys. 6 (1986), 17-44) for flows on compact surfaces.

Interval exchange transformations and foliations on infinite genus 2-manifolds

“…The examples constructed in this paper enhance the structure and smoothing results for orientable foliations with an arbitrary closed set of singularities on infinite genus 2-manifolds obtained by López [Lo1,Lo2]. Let us state the results of López which extend the structure and smoothing theorems for compact manifolds of Gutierrez [Gu].…”