Almost periodicity in semiflows

Seifert, George

doi:10.1090/S0002-9939-1995-1301527-9

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

On chaos in general semiflows

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