2019
Том 71
№ 2

All Issues

Slyusarchuk V. V.

Articles: 3
Brief Communications (Ukrainian)

Conditions for Instability of an Invariant Toroidal Manifold of a Discrete Dynamical System in a Banach Space

Slyusarchuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 572-576

We obtain conditions for the instability of an invariant toroidal manifold of a discrete dynamic system.

Article (Russian)

Discrete dynamical systems with invariant asymptotically stable toroidal manifold

Samoilenko A. M., Slyusarchuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 4. - pp. 466–471

We obtain conditions for asymptotic stability of quasiperiodic trajectories of discrete dynamical systems in the case of infinite-dimensional Banach space.

Article (Russian)

Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

Samoilenko A. M., Slyusarchuk V. E., Slyusarchuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1661–1676

We investigate the behavior of a diserete dynamical system in a neighborhood of a quasiperiodic trajeetory for the case of an infinite-dimensional Banach space We find conditions sufficient for the system considered to reduce, in such a neighborhood, to a system with quasiperiodic coefficients.