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Invariant sets of extensions of dynamical systems on manifolds
Grod Ivan Mykolayovych 1 , Kulyk V. 2
1 Department of mathematics and methods of its teaching, Ternopil National Pedagogical University named after Volodymyr Hnatyuk, Ternopil, 46027, Ukraine
2 Silesian University of Technology, Gliwice, 44, Poland
Keywords: Invariant sets
Abstract

We obtain sufficient conditions for the existence of bounded invariant manifolds for certain extensions of dynamical systems on the manifolds.

References

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.

Cite
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.
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