Abstract
Conditions for exponential stability and dichotomy of pulse linear extensions of dynamical systems on a torus are investigated.
References
A. M. Samoilenko, “On some problems of the theory of perturbations for smooth invariant tori of dynamical systems,” Ukr. Mat. Zh., 46, No. 12, 1665–1700 (1994).
V. I. Tkachenko, “The Green function and conditions of the existence of invariant sets of pulse systems,” Ukr. Mat. Zh., 41, No. 10, 1379–1383 (1989).
A. M. Samoilenko and N. I. Perestyuk, Differential Equations with Pulse Action [in Russian], Vyshcha Shkola, Kiev (1987).
A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 451–453, March, 1998.
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Yanchuk, S.V., Ali, N.A. Conditions for exponential stability and dichotomy of pulse linear extensions of dynamical systems on a torus. Ukr Math J 50, 514–516 (1998). https://doi.org/10.1007/BF02528818
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DOI: https://doi.org/10.1007/BF02528818