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Transactions of the American Mathematical Society

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The closing lemma for generalized recurrence in the plane


Author: Maria Lúcia Alvarenga Peixoto
Journal: Trans. Amer. Math. Soc. 308 (1988), 143-158
MSC: Primary 58F10; Secondary 34D30
DOI: https://doi.org/10.1090/S0002-9947-1988-0946436-0
MathSciNet review: 946436
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Abstract: We prove a version of the Closing Lemma for $ {C^r}$ vector fields on the plane, $ r \geqslant 1$, and for a kind of recurrence obtained using the concept of prolongational limit sets. We call it generalized recurrence.

Given a nonperiodic point $ p$ in the generalized recurrent set we perturb the vector field in order to get a new vector field arbitrarily close to it, with a closed orbit through $ p$.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0946436-0
Article copyright: © Copyright 1988 American Mathematical Society

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