Differential Equations

, Volume 44, Issue 10, pp 1406–1411

Time symmetry preserving perturbations of systems, and Poincaré mappings

  • V. I. Mironenko
  • V. V. Mironenko
Ordinary Differential Equations

DOI: 10.1134/S0012266108100066

Cite this article as:
Mironenko, V.I. & Mironenko, V.V. Diff Equat (2008) 44: 1406. doi:10.1134/S0012266108100066


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.

Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • V. I. Mironenko
    • 1
  • V. V. Mironenko
    • 1
  1. 1.Gomel State UniversityGomelBelarus

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