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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.

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References

  1. Krasnosel’skii, M.A., Operator sdviga po traektoriyam differentsial’nykh uravnenii (Operator of Shift Along Trajectories of Differential Equations), Moscow: Nauka, 1996.

    Google Scholar 

  2. Mironenko, V.I., Differ. Uravn., 1980, vol. 16, no. 11, pp. 1985–1994.

    MATH  MathSciNet  Google Scholar 

  3. Mironenko, V.I., Otrazhayushchaya funktsiya i periodicheskie resheniya differentsial’nykh uravnenii (Reflection Function and Periodic Solutions of Differential Equations), Minsk: Universitetskoe, 1986.

    Google Scholar 

  4. Al’sevich, L.A., Differ. Uravn., 1983, vol. 19, no. 8, pp. 1446–1449.

    MATH  MathSciNet  Google Scholar 

  5. Veresovich, P.P., Differ. Uravn., 1998, vol. 34, no. 10, pp. 1420–1422.

    MathSciNet  Google Scholar 

  6. Musafirov, E.V., Differ. Uravn., 2002, vol. 38, no. 4, pp. 570–572.

    MathSciNet  Google Scholar 

  7. Zhengxin Zhou, Nonlinear Analysis, 2003, vol. 53, no. 6, pp. 733–741.

    Article  MATH  MathSciNet  Google Scholar 

  8. Zhengxin Zhou, J. Math. Anal. Appl., 2003, vol. 278, no. 1, pp. 18–26.

    Article  MATH  MathSciNet  Google Scholar 

  9. Mironenko, V.V., Differ. Uravn., 2004, vol. 40, no. 10, pp. 1325–1332.

    MathSciNet  Google Scholar 

  10. Mironenko, V.I., Otrazhayushchaya funktsiya i issledovanie mnogomernykh differentsial’nykh sistem (Reflecting Function and the Investigation of Multidimensional Differential Systems), Gomel’: Gomel’skii Gos. Univ., 2004.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Gomel State University, Gomel, Belarus

    V. I. Mironenko & V. V. Mironenko

Authors
  1. V. I. Mironenko
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  2. V. V. Mironenko
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Additional information

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

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Mironenko, V.I., Mironenko, V.V. Time symmetry preserving perturbations of systems, and Poincaré mappings. Diff Equat 44, 1406–1411 (2008). https://doi.org/10.1134/S0012266108100066

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  • DOI: https://doi.org/10.1134/S0012266108100066

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