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

Published online by Cambridge University Press:  03 March 2005

AMÉRICO LÓPEZ
AMÉRICO LÓPEZ
Affiliation:
Universidade de São Paulo, FFCLRP-DFM, Av. Bandeirantes 3900, 14040-901, Ribeirão Preto, SP, Brazil (e-mail: amlopez@ffclrp.usp.br)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 3 , June 2005, pp. 893 - 912
Copyright
2005 Cambridge University Press