Literature cited
A. M. Samoilenko, “Necessary conditions for the existence of invariant tori of a linear extension of dynamical systems on the torus,” Differents. Uravn.,16, No. 8, 1428–1437 (1980).
A. M. Samoilenko, “Green's function of a linear extension of a dynamical system on a torus, conditions for its uniqueness, and properties following from these conditions,” Ukr. Mat. Zh.,32, No, 6, 791–797 (1980).
“Seminar on qualitative theory of differential equations at Moscow University,” Differents. Uravn.,15, No. 4, 750–761 (1979).
V. L. Kulik, “Conditionally stable invariant sets and manifolds of dynamical systems,” Author's Abstract of Candidate's Dissertation, Physical-Mathematical Sciences, Kiev (1975).
Y. Sibuya, “Some global properties of matrices of functions of one variable,” Math. Ann.,161, No. 1, 67–77 (1965).
A. M. Samoilenko and V. L. Kulik, “Exponential dichotomicity of invariant tori of dynamical systems,” Usp. Mat. Nauk,33, No. 3(201), 129–130 (1978).
A. M. Samoilenko, “Preservation of an invariant torus under perturbations,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, 1219–1240 (1970).
A. M. Samoilenko and V. L. Kulik, “Exponential dichotomy of an invariant torus of dynamical systems,” Differents. Uravn.,15, No. 8, 1434–1443 (1979).
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc. (1974).
V. L. Kulik, “The question of dependence of Green's functions of a problem on the invariant torus of a parameter,” Ukr. Mat. Zh.,30, No. 5, 545–551 (1978).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 33, No. 1, pp. 31–38, January–February, 1981.
Rights and permissions
About this article
Cite this article
Samoilenko, A.M. Separatrice manifolds and decomposability of a linear extension of a dynamical system on the torus. Ukr Math J 33, 23–29 (1981). https://doi.org/10.1007/BF01085770
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01085770