Ordinary Differential Equations

Differential Equations

, Volume 44, Issue 10, pp 1406-1411

First online:

Time symmetry preserving perturbations of systems, and Poincaré mappings

  • V. I. MironenkoAffiliated withGomel State University
  • , V. V. MironenkoAffiliated withGomel State University

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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.