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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The closing lemma for generalized recurrence in the plane
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by Maria Lúcia Alvarenga Peixoto PDF
Trans. Amer. Math. Soc. 308 (1988), 143-158 Request permission

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 $p$.
References
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • 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