Slyusarchuk V. V.
Conditions for Instability of an Invariant Toroidal Manifold of a Discrete Dynamical System in a Banach Space
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.
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.
Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution
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.