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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The planar closing lemma for chain recurrence


Authors: Maria Lúcia Alvarenga Peixoto and Charles Chapman Pugh
Journal: Trans. Amer. Math. Soc. 341 (1994), 173-192
MSC: Primary 58F30; Secondary 58F20, 58F25
MathSciNet review: 1107028
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Abstract: If $ z$ is a chain recurrent point of a $ {C^r}$ planar flow, all of whose fixed points are hyperbolic, then it is proved that the orbit through $ z$ becomes periodic under a perturbation that is $ {C^r}$ small in the Whitney topology.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1107028-9
PII: S 0002-9947(1994)1107028-9
Article copyright: © Copyright 1994 American Mathematical Society