## Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions

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- by Konstantin Mischaikow, Hal Smith and Horst R. Thieme
- Trans. Amer. Math. Soc.
**347**(1995), 1669-1685 - DOI: https://doi.org/10.1090/S0002-9947-1995-1290727-7
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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.## References

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## Bibliographic 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