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Smoothing continuous flows on two-manifolds and recurrences

Published online by Cambridge University Press:  19 September 2008

Carlos Gutierrez
Carlos Gutierrez
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22.460-Rio de Janeiro-RJ-Brasil
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Abstract

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Let φ: ℝ × M → M be a continuous flow on a compact C∞ two-manifold M. It is proved that there exists a C1 flow ψ on M which is topologically equivalent to φ, and that the following conditions are equivalent:

(a) any minimal set of φ is trivial;

(b) φ is topologically equivalent to a C2 flow;

(c) φ is topologically equivalent to a C∞ flow.

Also proved is a structure and an existence theorem for continuous flows with non-trivial recurrence.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 17 - 44
Copyright
Copyright © Cambridge University Press 1986

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