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Linear extensions of dynamical systems on a torus that possess Green-Samoilenko functions

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Abstract

By using Lyapunov functions with alternating signs, we study problems of regularity and weak regularity for some linear extensions of dynamical systems on a torus.

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References

  1. A. M. Samoilenko, “On the preservation of an invariant torus under perturbation,” Izv. Akad. Nauk SSSR, Ser. Mat., 34, No. 6, 1219–1240 (1970).

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  2. Yu. A. Mitropol’skii, A. M. Samoilenko, and V. L. Kulik, Investigation of Dichotomy of Linear Systems of Differential Equations with the Use of Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).

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  3. A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).

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  4. A. M. Samoilenko, “Separatrix manifolds and decomposability of linear extensions of dynamical systems on a torus,” Ukr. Mat. Zh., 33, No. 1, 31–38 (1981).

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Authors and Affiliations

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

    V. L. Kulik

  2. Szlensk Polytechnics, Glivitse, Poland

    V. L. Kulik

  3. Lyublin Polytechnics, Lyublin, Poland

    B. Wojtowicz

Authors
  1. V. L. Kulik
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  2. B. Wojtowicz
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 178–188, February, 1998.

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Kulik, V.L., Wojtowicz, B. Linear extensions of dynamical systems on a torus that possess Green-Samoilenko functions. Ukr Math J 50, 203–215 (1998). https://doi.org/10.1007/BF02513446

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  • DOI: https://doi.org/10.1007/BF02513446

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