Almost periodicity in semiflows
HTML articles powered by AMS MathViewer
- by George Seifert PDF
- Proc. Amer. Math. Soc. 123 (1995), 2895-2899 Request permission
Abstract:
For a semiflow on a complete metric space we show that if a semiorbit has compact closure and its positive limit set consists of stable points, the orbit is asymptotically almost periodic. Under stronger hypotheses which are more tractable in applications, the same conclusion holds. An application to a scalar delay-differential equation is given.References
- Hal L. Smith and Horst R. Thieme, Quasi convergence and stability for strongly order-preserving semiflows, SIAM J. Math. Anal. 21 (1990), no. 3, 673–692. MR 1046795, DOI 10.1137/0521036
- Hal L. Smith and Horst R. Thieme, Convergence for strongly order-preserving semiflows, SIAM J. Math. Anal. 22 (1991), no. 4, 1081–1101. MR 1112067, DOI 10.1137/0522070 G. Seifert, On chaos in general semiflows, submitted for publication.
- A. S. Besicovitch, Almost periodic functions, Dover Publications, Inc., New York, 1955. MR 0068029
- A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799, DOI 10.1007/BFb0070324
- Jack K. Hale, Functional differential equations, Analytic theory of differential equations (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1970) Lecture Notes in Mat., Vol. 183, Springer, Berlin, 1971, pp. 9–22. MR 0390425
- V. V. Nemytskii and V. V. Stepanov, Qualitative theory of differential equations, Princeton Mathematical Series, No. 22, Princeton University Press, Princeton, N.J., 1960. MR 0121520
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2895-2899
- MSC: Primary 34C35; Secondary 34C27, 34K15, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301527-9
- MathSciNet review: 1301527