2017
Том 69
№ 9

All Issues

On the stability of an invariant torus

Dudzyanyi S. I., Perestyuk N. A.

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Abstract

We consider the problem of the asymptotic stability for trivial invariant torus of a linear extension of dynamical system on a torus. We formulate and prove sufficient criteria of asymptotic stability and study conditions for the existence and uniqueness of the Lyapunov functions of fixed sign.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 9, pp 1365-1376.

Citation Example: Dudzyanyi S. I., Perestyuk N. A. On the stability of an invariant torus // Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1212-1222.

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