Abstract:
There is presented a new approach to the theory of perturbation of invariant toroidal manifolds of dynamical systems related to use of Green's functions for a linearized problem. This approach permits the presentation, from a single and general point of view, of the theory of perturbation of smooth as well as of nondifferentiable invariant manifolds of dynamical systems, and also permits the proof of new theorems on the existence of such manifolds.
\Bibitem{Sam70}
\by A.~M.~Samoilenko
\paper Preservation of an invariant torus under perturbation
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 6
\pages 1225--1249
\mathnet{http://mi.mathnet.ru/eng/im2468}
\crossref{https://doi.org/10.1070/IM1970v004n06ABEH000954}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=299910}
\zmath{https://zbmath.org/?q=an:0224.34043}
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https://www.mathnet.ru/eng/im2468
https://doi.org/10.1070/IM1970v004n06ABEH000954
https://www.mathnet.ru/eng/im/v34/i6/p1219
This publication is cited in the following 8 articles:
V. L. Kulyk, H. M. Kulyk, N. V. Stepanenko, “On Some Constructions of Regular Linear Extensions of Dynamical Systems on a Torus”, J Math Sci, 278:6 (2024), 1013
I. M. Hrod, V. L. Kulyk, “Construction of Lyapunov Functions in the Form of Pencils of Quadratic Forms”, J Math Sci, 243:2 (2019), 183
A. M. Samoilenko, “Smoothness in the parameter of an invariant torus of a quasilinear system of differential equations”, Ukr Math J, 38:5 (1987), 516
A. M. Samoilenko, V. L. Kulik, “On the existence of the Green function of the problem of the invariant torus”, Ukr Math J, 27:3 (1976), 279
V. L. Golets, “Asymptotic integration of certain weakly nonlinear systems”, Ukr Math J, 24:3 (1973), 331
Yu. A. Mitropol'skii, A. M. Samoilenko, “Quasi-periodic oscillations in linear systems”, Ukr Math J, 24:2 (1973), 144
A. M. Samoilenko, “On the reduction to canonical form of a dynamical system in the neighborhood of a smooth invariant torus”, Math. USSR-Izv., 6:1 (1972), 211–234
V. L. Golets, “Perturbation of a stable invariant torus of a dynamical system”, Ukr Math J, 23:1 (1972), 117
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