Перейти до основного вмісту
Smoothness of invariant manifolds of nonlinear Riccati-type systems
Grod Ivan Mykolayovych 1
1 Department of mathematics and methods of its teaching, Ternopil National Pedagogical University named after Volodymyr Hnatyuk, Ternopil, 46027, Ukraine
Keywords: invariant manifolds, nonlinear Riccati-type systems
Abstract
The properties of smoothness of invariant manifolds of toroidal of nonlinear systems of type Riccati are studied.
References

[1]  Mozer J.J. On invariant curves of area-preserving mappings of an annulus // Nachr. Acad. Wiss. Gottingen Math.-Phis. Kl. 1962. Vol. 18a, N 1.P. 1 - 20.

[2]  Sacker R.J. A perturbation theorem for invariant manifolds and Holder continuity // J. Math. and Mech. 1969. Vol.18, N 8. P. 705 - 762.

[3] Samoilenko A.M. On the conservation of the invariant torus under perturbation // Izv. of the USSR Academy of Sciences. Ser.mat. 1970. Т.34, №6. P. 1219-1240.

[4] Mitropolskiy Y. A., Samoilenko A. A. M.,Kulik V. L. Investigation of dichotomy of systems of linear differential equations by means of Lyapunov function. Kiev, 1990.

[5] Mitropolskiy Y.A., Grod I.N.Some problems of invariant manifolds of invariant Lyapunov functions.  - Kiev, 1989.-37p.-(Prepr./AN UkrSSR. Institute of Mathematics)

[6] Samoilenko A.M., Burylko A.A., Grod I.N. Continuity modules of derivatives of invariant tori of linear extensions of dynamical systems// Differential Equations. 2000. Т. 36, №1. P.103-113.

[7] Bronshinein I.U., Kopanskii A.Ya. Invariant manifold and normal forms.- Kishinev, 1992. 

[8] I.N. Rodin, V.L. Kulik, On properties of continuity of invariant tori and Green's function of linear extensions on a torus// Ukr. mat. zhurn. 1998.Vol.41, №.12. P. 1709 - 1714.

[9] Samoilenko, A.M., Kulik, V.L. On the properties of matrixants influencing the regularity of linear extensions of dynamical systems on the torus  // Differential Equations. 1997. Т.30, №6. P. 779 - 788.

[10] Samoilenko A.M., Burilko A.A. The question of smoothness of Green's functions in the problem of bounded manifolds // Ukrainian Mathematical Journal 1998. Т. 51, №4. P. 570 - 584.

Cite
ACS Style
Grod , I.M. Smoothness of invariant manifolds of nonlinear Riccati-type systems. Bukovinian Mathematical Journal. 2016, 3
AMA Style
Grod IM. Smoothness of invariant manifolds of nonlinear Riccati-type systems. Bukovinian Mathematical Journal. 2016; 3(3-4).
Chicago/Turabian Style
Ivan Mykolayovych Grod . 2016. "Smoothness of invariant manifolds of nonlinear Riccati-type systems". Bukovinian Mathematical Journal. 3 no. 3-4.
Export
We use own, third-party cookies, and localStorage files to analyze web traffic and page activities. Privacy Policy Settings