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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Abstract $\omega$-limit sets, chain recurrent sets, and basic sets for flows
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by John E. Franke and James F. Selgrade PDF
Proc. Amer. Math. Soc. 60 (1976), 309-316 Request permission

Abstract:

An abstract $\omega$-limit set for a flow is an invariant set which is conjugate to the $\omega$-limit set of a point. This paper shows that an abstract $\omega$-limit set is precisely a connected, chain recurrent set. In fact, an abstract $\omega$-limit set which is a subset of a hyperbolic invariant set is the $\omega$-limit set of a nearby heteroclinic point. This leads to the result that a basic set is a hyperbolic, compact, invariant set which is chain recurrent, connected, and has local product structure.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 309-316
  • MSC: Primary 58F20; Secondary 58F10
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0423423-X
  • MathSciNet review: 0423423