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A counter-example to a C2 closing lemma

Published online by Cambridge University Press:  19 September 2008

C. Gutierrez
C. Gutierrez
Affiliation:
IMPA, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ, CEP 22 460, Brazil
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Abstract

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Let M be a compact manifold that contains a two-dimensional punctured torus. Given p ∈ M and an integer r ≥ 2, there exists X ∈ ∞(M) having non-trivial recurrent trajectories and such that, for some neighbourhood of X|(M−{p}) in r(M−{p}), no Y ∈ has closed orbits.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 4 , December 1987 , pp. 509 - 530
Copyright
Copyright © Cambridge University Press 1987

References

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