On the hyperbolicity of rapidly oscillating periodic solutions of functional differential equations

We consider periodic solutions of nonlinear functional differential equations with rational periods less than 2. We study the spectral properties of monodromy operators and state a hyperbolicity criterion for such solutions.__________Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 82–85, 2005Original Russian Text Copyright © by A. L. Skubachevskii and H.-O. WaltherThe first authors research was supported by the Mercator-Programm of the Deutsche Forschungsgemeinschaft, RFBR grant No. 04-01-00256, and Russian Ministry of Education and Science grant No. E02-1.0-131.Translated by A. L. Skubachevskii and H.-O. Walther