Abstract
We study a discrete system in a neighborhood of a quasi-periodic trajectory. We obtain conditions for reducing a system in this neighborhood to a system with quasi-periodic coefficients. We determine the behavior of this system under the action of small perturbations.
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A. M. Samoilenko, “Investigation of dynamic systems in a neighborhood of a quasi-periodic trajectory,” Preprint 90.35, Akad. Nauk Ukr. SSR, Inst. Mat. (1990).
A. M. Samoilenko, “Dynamic systems in δm × En,” Ukr. Mat. Zh.,43, No. 10, 1283–1298 (1991).
Yu. A. Mitropol'skii, A. M. Samoilenko, and D. I. Martynyuk, Systems of Evolution Equations with Periodic and Conditionally Periodic Coefficients [in Russian], Naukova Dumka, Kiev (1984).
A. Halanay and D. Wexler, The Qualitative Theory of Systems with Impulse [Russian translation], Mir, Moscow (1971).
Yu. I. Neimark, The Method of Point Transformations in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1972).
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This work was prepared with the financial support of the Ukrainian State Committee on Science and Technology.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 12, pp. 1702–1711, December, 1992.
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Samoilenko, A.M. Study of a discrete dynamic system in a neighborhood of a quasi-periodic trajectory. Ukr Math J 44, 1560–1568 (1992). https://doi.org/10.1007/BF01061281
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DOI: https://doi.org/10.1007/BF01061281