Some constructions of Lyapunov function for linear extensions of dynamical systems

• Autorzy: Kulik V. , Tkocz-Piszczek E.
• Języki publikacji: EN

Abstrakty

EN

In this note we consider some sets of linear extensions of dynamical systems and research regularity by means of the sign-changing Lyapunov function. We examine some constructions of Lyapunov functions for given systems.

Słowa kluczowe

EN

Lyapunov function; invariant manifold; invariant torus

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 3
• Strony: 399--409
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kulik V.

autor

Tkocz-Piszczek E.

• Silesian University of Technology Department of Mathematics ul. Kaszubska 23, Gliwice, Poland,

Bibliografia

• [1] Yu.A. Mitropolsky, A.M. Samoilenko, V.L. Kulik, Dichotomies and Stability in Nonautonomous Linear Systems, Taylor&Francis Inc., London, 2003.
• [2] B.I. Moseenkov, P.A. Maksimyuk, Studying parametric resonance when semiconductor crystals are illuminated by modulated light, Naukova Dumka, Kiev, 1977 [in Russian].
• [3] N.W. Stiepanenko, E. Tkocz-Piszczek, Problems of regularity of linear extensions of dynamical systems on a torus, Nonlinear Oscil. 12 (2009), 99–109.
• [4] V.L. Kulik, N.W. Stiepanenko, Alternating-sign Lyapunov functions in the theory of linear extensions of dynamical systems on a torus, Ukrain. Mat. Zh. 59 (2007) 4, 489–500; translation in Ukrainian Math. J. 59 (2007) 4, 546–562 [in Ukrainian].
• [5] H.M. Kulik, V.L. Kulik, Existence of Green-Samoilenko functions of some linear extensions of dynamical systems, Nonlinear Oscill. 7 (2004), 468–474.
• [6] A.A. Boichuk, A condition for the existence of a unique Green–Samoilenko function for the problem of invariant torus, Ukrainian Math. J. 53 (2001), 556–559.
• [7] A.M. Samoilenko, On the existence of a unique Green function for the linear extension of a dynamical system on a torus, Ukrainian Math. J. 53 (2001), 513–521.