Frequency entrainment for almost periodic evolution equations
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- by James Murdock PDF
- Proc. Amer. Math. Soc. 96 (1986), 626-628 Request permission
Abstract:
A theorem of Massera stating that periodic solutions of equations are (under a simple hypothesis) entrained is generalized to limit periodic equations and (with a weak definition of entrainment) to almost periodic equations. An error is explained in a stronger result claimed by Cartwright.References
- A. S. Besicovitch, Almost periodic functions, Dover Publications, Inc., New York, 1955. MR 0068029
- M. L. Cartwright, Almost periodic differential equations and almost periodic flows, J. Differential Equations 5 (1969), 167–181. MR 239191, DOI 10.1016/0022-0396(69)90110-7 N. Forbat, Amalytische Mechanik der Schwingungen, V.E.B. Deutsche Verlag der Wissenschaft, Berlin, 1966. P. Hagedorn, Non-linear oscillations, translated by W. Stadler, Clarendon Press, Oxford, 1981.
- José L. Massera, Remarks on the periodic solutions of differential equations, Bol. Fac. Ingen. Montevideo 4 (1950), no. (Año 14) (Spanish). MR 47866
- G. C. O’Brien, The frequencies of almost periodic solutions of almost periodic differential equations, J. Austral. Math. Soc. 17 (1974), 332–344. Collection of articles dedicated to the memory of Hanna Neumann, VII. MR 0357979
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 626-628
- MSC: Primary 34C27; Secondary 35B15
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826492-4
- MathSciNet review: 826492