Abstract
Conditions are considered under which any trajectory from a small neighborhood of a torus of a nonlinear countable system of differential equations is attacted to a corresponding trajectory on the torus by an exponential law.
This is a preview of subscription content, log in via an institution to check access.
Literature cited
A. M. Samoilenko, “Preserving an invariant torus under a perturbation,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 6, 1219–1240 (1970).
A. M. Samoilenko, “Exponential stabilist of an invariant torus of a dynamical system,” Differents. Uravn.,11, No. 5, 820–834 (1975).
A. M. Samoilenko, Yu. V. Teplinskii, and N. S. Tsyganovskii, “Invariant tori of countable systems of differential equations,” Kiev, 1983 (Preprint Akad. Nauk UkrSSR, Inst. Mat. 83.30).
P. I. Avdeyuk, “Behavior of solutions of a quasilinear countable system of differential equations in a neighborhood of an invariant torus,” in: Asymptotic Integration of Differential Equations [in Russian], Inst. Mat. Akad. Nauk UkrSSR, Kiev (1985), pp. 3–8.
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 401–405, March, 1990.
Rights and permissions
About this article
Cite this article
Teplinskii, Y.V., Avdeyuk, P.I. Exponential stability of an invariant torus of a nonlinear countable system of differential equations. Ukr Math J 42, 357–360 (1990). https://doi.org/10.1007/BF01057025
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01057025