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Frequency entrainment for almost periodic evolution equations


Author: James Murdock
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
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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 [Enhancements On Off] (What's this?)

  • [1] A. S. Besicovitch, Almost periodic functions, Dover Publications, Inc., New York, 1955. MR 0068029
  • [2] M. L. Cartwright, Almost periodic differential equations and almost periodic flows, J. Differential Equations 5 (1969), 167–181. MR 0239191, https://doi.org/10.1016/0022-0396(69)90110-7
  • [3] N. Forbat, Amalytische Mechanik der Schwingungen, V.E.B. Deutsche Verlag der Wissenschaft, Berlin, 1966.
  • [4] P. Hagedorn, Non-linear oscillations, translated by W. Stadler, Clarendon Press, Oxford, 1981.
  • [5] José L. Massera, Remarks on the periodic solutions of differential equations, Bol. Fac. Ingen. Montevideo 4 (1950), no. (Año 14), 37–45 = 43–53 Facultad de Ingeniería Montevideo. Publ. Inst. Mat. Estadística 2, 43–53 (1950) (Spanish). MR 0047866
  • [6] 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

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DOI: https://doi.org/10.1090/S0002-9939-1986-0826492-4
Article copyright: © Copyright 1986 American Mathematical Society

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