2019
Том 71
№ 11

All Issues

Marchuk N. A.

Articles: 2
Article (Ukrainian)

On the Fréchet Differentiability of Invariant Tori of Countable Systems of Difference Equations Defined on Infinite-Dimensional Tori

Marchuk N. A., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 75-90

By using the method of Green–Samoilenko functions, in the space of bounded number sequences we construct invariant tori of linear and nonlinear systems of discrete equations defined on infinite-dimensional tori. We establish sufficient conditions for the Fréchet differentiability of invariant tori.

Article (Ukrainian)

On the Smoothness of the Invariant Torus of a Countable System of Difference Equations with Parameters

Marchuk N. A., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 9. - pp. 1241-1250

We establish sufficient conditions for the differentiability of the invariant torus of a countable system of linear difference equations defined on a finite-dimensional torus with respect to an angular variable and the parameter of the original system of equations.