Regularity of matrix differential equations

Grod  Ivan Mykolayovych; Kulyk V.

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: matrix differential equations

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Abstract

We study the existence of bounded invariant manifolds for some linear extensions of dynamical systems.

References

[1] Mitropolsky Y.A., Samoilenko A.M., Kulik V.L. Investigation of dichotomy of linear systems of differential equations by means of Lyapunov functions. - Kiev: Nauk.dumka, 1990. - 270 p.

[2] Yu. A. Mitropolsky, A. M. Samoilenko, V. L. Kulik Dichotomies and Stability in Nonautonomous Linear Systems. place CityTaylor & Francis Inc, placeCityLondon, 2004.

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

[4] Samoylenko A.M. To the question of existence of a single Green's function of linear expansion of a dynamical system on a torus // Ukr.mat.zhurn., - 2001. -53, №4. - P. 513-521.

[5] Boychuk A.A. Existence condition of the singular Green-Samoilenko function of the invariant torus problem // Ukr.mat.zhurn, -2001. -53, №4. - P. 556-559.

[6] Grod I.M., Kulyk V.I. Construction of Lyapunov functions of some linear expansions of dynamic systems // Lviv Univ. Series of Mech.-Mat., - 2010. - Issue 72. - P. 79-93.

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ACS Style: Grod , I.M.; Kulyk, V. Regularity of matrix differential equations. Bukovinian Mathematical Journal. 2016, 1
AMA Style: Grod IM, Kulyk V. Regularity of matrix differential equations. Bukovinian Mathematical Journal. 2016; 1(1-2).
Chicago/Turabian Style: Ivan Mykolayovych Grod , V. Kulyk. 2016. "Regularity of matrix differential equations". Bukovinian Mathematical Journal. 1 no. 1-2.

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