We obtain sufficient conditions for the existence of bounded invariant manifolds for certain extensions of dynamical systems on the manifolds.
Mozer J.J.Oninvariantcurvesofarea-preserving mappings of an annulus // Nachr. Acad. Wiss. Gottingen Math.-Phis. Kl. 1962. Vol. 18a, N 1.P. 1 – 20.
Sacker R.J.Aperturbationtheoremforinvariant manifoldsandHoldercontinuity//J.Math.andMech. 1969. Vol.18, N 8. P. 705 – 762.
Samoylenko A.M. On preservation of an invariant torus under perturbation // Izv. AN SSSR. Ser. Mat. 1970. Vol. 34, No. 6. P. 1219-1240.
Samoilenko A.M. Elements of the mathematical theory of multifrequency oscillations. – M.: Nauka, – 1987. – 304 p.
Perestyuk M.O., Slyusarchuk V.Yu. The Green-Samoylenko operator in the theory of invariant sets of nonlinear differential equations // Ukr. Mat. Zh. 2008. Vol. 60, No. 7. WITH. 948 - 957.
Mitropolskyi Yu.A., Samoilenko A.M., Kulyk V.L. Investigation of the dichotomy of linear systems of differential equations using Lyapunov functions – Kyiv: Nauk. Dumka, 1990. – 272 p.
Bronstein I.U., Kopansky A.Ya. Invariant manifold and normal forms. - Shtiintsa: Chisinau, 1992. - 330 p.
Grod I.N., Kulyk V.L. On properties of continuity of invariant tori and Green's function of linear extended tori// Ukr. mate. journal 1998. Vol. 41, No. 12. WITH. 1709 - 1714.
Kolmogorov A.N., Fomin S. IN. Elements of the theory of functions and functional analysis. - M.: Nauka, 1968. - 496 p.
- ACS Style
- Grod , I.M.; Kulyk, V. Invariant sets of extensions of dynamical systems on manifolds. Bukovinian Mathematical Journal. 2017, 5
- AMA Style
- Grod IM, Kulyk V. Invariant sets of extensions of dynamical systems on manifolds. Bukovinian Mathematical Journal. 2017; 5(1-2).
- Chicago/Turabian Style
- Ivan Mykolayovych Grod , V. Kulyk. 2017. "Invariant sets of extensions of dynamical systems on manifolds". Bukovinian Mathematical Journal. 5 no. 1-2.