, Volume 44, Issue 10, pp 1406-1411
Date: 28 Nov 2008

Time symmetry preserving perturbations of systems, and Poincaré mappings

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Abstract

In the present paper, we obtain necessary and sufficient conditions under which two differential systems have the same symmetries described by a reflecting function. Under these conditions, the systems in question have a common shift operator along solutions of these systems on a symmetric time interval [−ω, ω]. Therefore, the mappings over the period [−ω, ω] coincide for such systems provided that these systems are 2ω-periodic.

Original Russian Text © V.I. Mironenko, V.V. Mironenko, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 10, pp. 1347–1352.