2017
Том 69
№ 9

All Issues

On Some Properties of the Behavior of Linear Extensions of Dynamical Systems on a Torus under Perturbation of Phase Variables

Samoilenko A. M., Stepanenko N. V.

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Abstract

We investigate classes of linear extensions of dynamical systems on a torus for which the Lyapunov functions exist for an arbitrary flow on the torus. Linear extensions for which the Lyapunov functions exist only with varying coefficients are considered separately. We investigate the problem of preservation of regularity under perturbation of phase variables.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 3, pp 504-510.

Citation Example: Samoilenko A. M., Stepanenko N. V. On Some Properties of the Behavior of Linear Extensions of Dynamical Systems on a Torus under Perturbation of Phase Variables // Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 408-412.

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