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

 

Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions


Authors: Konstantin Mischaikow, Hal Smith and Horst R. Thieme
Journal: Trans. Amer. Math. Soc. 347 (1995), 1669-1685
MSC: Primary 34C35; Secondary 34D05, 34K20, 54H20
MathSciNet review: 1290727
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1290727-7
PII: S 0002-9947(1995)1290727-7
Keywords: Chain recurrence, asymptotically autonomous semiflow, Lyapunov function
Article copyright: © Copyright 1995 American Mathematical Society