On the existence of invariant tori of countable systems of difference-differential equations defined on infinite-dimensional tori
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In the space of bounded number sequences, we establish sufficient conditions for the existence of invariant tori for linear and quasilinear countable systems of differential-difference equations defined on infinitedimensional tori and containing an infinite set of constant deviations of a scalar argument.
KeywordsCountable System Invariant Torus Ukrainian National Academy Constant Deviation Arbitrary Real Number
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- 1.A. M. Samoilenko, “On perturbation theory of invariant manifolds of dynamical systems,” in: Proceedings of the Fifth International Conference on Nonlinear Oscillations, Vol. 1, Analytic Methods [in Russian], Institute of Mathematics, Academy of Sciences of Ukr. SSR, Kiev (1970), pp. 495–499.Google Scholar
- 3.A. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations [in Russian], Institute Mathematics, Ukrainian National Academy of Sciences, Kiev (1993).Google Scholar
- 7.A. A. El’nazarov, Some Problems of the Theory of Countable Systems and Asymptotic Methods [in Ukrainian], Candidate-Degree Thesis (Physics and Mathematics), Kyiv (1998).Google Scholar
- 8.B. Kh. Zhanbusinova, Quasiperiodic Solutions of Countable Systems of Difference-Differential Equations [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Kiev (1991).Google Scholar
- 9.D. I. Martynyuk and H. V. Ver’ovkina, “Invariant sets of countable systems of difference equations,” Visn. Kyiv Univ., Ser. Fiz.-Mat. Nauk, Issue 1, 117–127 (1997).Google Scholar
- 10.D. I. Martynyuk, V. I. Kravets, and B. Kh. Zhanbusinova, “On an invariant torus of a countable system of differential equations with delay,” in: Asymptotic Methods in Problems of Mathematical Physics [in Russian], Institute of Mathematics, Academy Sciences of Ukr. SSR, Kiev (1989), pp. 77–86.Google Scholar
- 12.Yu. V. Teplins’kyi and N. A. Marchuk, “On the Cρ-smoothness of an invariant torus of a countable system of difference equations defined on an m-dimensional torus,” Nelin. Kolyvannya, 5, No. 2, 251–265 (2002).Google Scholar
- 13.Yu. V. Teplins’kyi and N. A. Marchuk, “On the Fréchet differentiability of invariant tori of countable systems of difference equations defined on infinite-dimensional tori,” Ukr. Mat. Zh., 55, No. 1, 75–90 (2003).Google Scholar
- 14.A. M. Samoilenko, Yu. V. Teplins’kyi, and I. V. Semenyshyna, “On the existence of a smooth bounded semiinvariant manifold for a degenerate nonlinear system of difference equations in the space m;” Nelin. Kolyvannya, 6, No. 3, 378–400 (2003).Google Scholar