Abstract
Under the assumption that a linear homogeneous system defined on the direct product of a torus and a Euclidean space is exponentially dichotomous on the semiaxes, we obtain a condition for the existence of a unique Green–Samoilenko function for the problem of invariant torus. We find an expression for this function in terms of projectors that determine the dichotomy on the semiaxes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).
K. J. Palmer, “Exponential dichotomies and transversal homoclinic points,” J. Different. Equat., 55, 225–256 (1984).
A. A. Boichuk, “Solutions of weakly nonlinear differential equations bounded on the whole line,” Nelin. Kolyv., 2, No. 1, 3–10 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Boichuk, A.A. A Condition for the Existence of a Unique Green–Samoilenko Function for the Problem of Invariant Torus. Ukrainian Mathematical Journal 53, 637–641 (2001). https://doi.org/10.1023/A:1012386923624
Issue Date:
DOI: https://doi.org/10.1023/A:1012386923624