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On necessary conditions for the weak regularity of a linear extension of a dynamical system on a torus

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Abstract

We give a necessary condition for the weak regularity of a linear extension of a dynamical system on a torus in the form of Fourier series with respect to a part of the variables.

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References

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

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  2. A. M. Samoilenko and V. L. Kulik, “On the regularity of differential equations being linearized in a part of the variables,” Differents. Uravn., 31, No. 5, 773–777 (1995).

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Authors and Affiliations

  1. Kiev Polytechnical Institute, Kiev

    A. L. Grechko

Authors
  1. A. L. Grechko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 424–425, March, 1998.

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Grechko, A.L. On necessary conditions for the weak regularity of a linear extension of a dynamical system on a torus. Ukr Math J 50, 481–483 (1998). https://doi.org/10.1007/BF02528812

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  • DOI: https://doi.org/10.1007/BF02528812

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