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On the Cr-closing lemma for flows on the torus T2

Published online by Cambridge University Press:  19 September 2008

C. Gutierrez
C. Gutierrez
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, Jardim Botânico, Rio de Janeiro, RJ CEP 22.460, Brazil
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Abstract

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Vector fields of , 1 ≤ r ≤ ∞, with non-trivial recurrent points are classified in two types, one of which we call the constant type inspired by the terminology of continued fractions. Let have finitely many singularities and p ∈ T2 be a non-wandering point of X. With the exception of the case when X is of constant type and, simultaneously, p is non-trivial recurrent, we prove that there exists arbitrarily close to X (in the Cr-topology) having a periodic trajectory through p.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 45 - 56
Copyright
Copyright © Cambridge University Press 1986

References

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