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Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

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Abstract

We investigate the behavior of a diserete dynamical system in a neighborhood of a quasiperiodic trajeetory for the case of an infinite-dimensional Banach space We find conditions sufficient for the system considered to reduce, in such a neighborhood, to a system with quasiperiodic coefficients.

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Authors and Affiliations

  1. Ukrainian Academy of Sciences, Kiev

    A. M. Samoilenko

  2. Ukrainian State Academy of Water Economy, Rivne

    A. M. Samoilenko & V. E. Slyusarchuk

  3. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. V. Slyusarchuk

Authors
  1. A. M. Samoilenko
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  2. V. E. Slyusarchuk
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  3. V. V. Slyusarchuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1661–1676, December, 1997.

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Samoilenko, A.M., Slyusarchuk, V.E. & Slyusarchuk, V.V. Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution. Ukr Math J 49, 1872–1890 (1997). https://doi.org/10.1007/BF02513066

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