Construction of Lyapunov Functions in the Theory of Regular Linear Extensions of Dynamical Systems on a Torus
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Lyapunov functions are considered in the form of linear combinations of quadratic forms. We study the conditions under which the linear extensions of dynamic systems on a torus are regular.
KeywordsCauchy Problem Quadratic Form Green Function Lyapunov Function Naukova Dumka
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- 1.A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Moscow, Nauka (1987).Google Scholar
- 2.A. M. Samoilenko, “On some problems in the perturbation theory of smooth invariant tori of dynamical systems,” Ukr. Mat. Zh., 46, No. 12, 1665–1699 (1994); English translation: Ukr. Math. J., 46, No. 12, 1848–1889 (1994).Google Scholar
- 3.A. M. Samoilenko, “On the existence of a unique Green function for the linear extension of a dynamical system on a torus,” Ukr. Mat. Zh., 53, No. 4, 513–521 (2001); English translation: Ukr. Math. J., 53, No. 4, 584–594 (2001).Google Scholar
- 4.Yu. A. Mitropol’skii, A. M. Samoilenko, and V. L. Kulik, Investigation of the Dichotomy of Linear Systems of Differential Equations with the Help of Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
- 5.A. A. Boichuk, “A condition for the existence of a unique Green–Samoilenko function for the problem of invariant torus,” Ukr. Mat. Zh., 53, No. 4, 556–559 (2001); English translation: Ukr. Math. J., 53, No. 4, 637–641 (2001).Google Scholar
- 6.V. L. Kulyk and N. V. Stepanenko, “Alternating Lyapunov functions in the theory of linear extensions of dynamical systems on a torus,” Ukr. Mat. Zh., 59, No. 4, 488–500 (2007); English translation: Ukr. Math. J., 59, No. 4, 546–562 (2007).Google Scholar