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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions
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by Konstantin Mischaikow, Hal Smith and Horst R. Thieme PDF
Trans. Amer. Math. Soc. 347 (1995), 1669-1685 Request permission

Abstract:

From the work of C. Conley, it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set. Here, we improve a result of L. Markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow. In the special case that there is a Lyapunov function for the limiting semiflow, sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the Lyapunov function.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1669-1685
  • MSC: Primary 34C35; Secondary 34D05, 34K20, 54H20
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1290727-7
  • MathSciNet review: 1290727