Investigation of a dynamical system in a neighborhood of an invariant toroidal manifold in the general case

A dynamical system is studied in the neighborhood of an invariant toroidal manifold for the most general relationship between the dimensionality of the phase space and the dimensionality of the manifold.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1399–1408, October, 1994.     

On representations of the Heisenberg relations for the quantumE(2) group

All irreducible^* -representations of the involutive algebraA generated by the so-called Heisenberg relations for the quantum deformation of the group of motions of the Euclidean plane are described.Dedicated to the 70th birthday of our teacher, Prof. Yu. M. BerezanskiiPublished in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 689–692, May, 1995.This research was partially supported by the Ukrainian State Committee on Science and Technology, the International Science Foundation, grant No. U6D000, and a grant from the American Mathematical Society.     

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

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.     

Averaging of Nonlinear Oscillation Systems of Higher Approximation with Delay

For oscillation resonance systems with delay on a finite segment or a semiaxis, we justify the averaging method with respect to fast variables. We also obtain error estimates for this method, which explicitly depend on a small parameter.     

N. N. Bogolyubov's research in mathematics and theoretical physics

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1156–1164, September, 1989.     

Oleksandr Ivanovych Stepanets' (On His 60th Birthday)

Ukrainian Mathematical Journal -     

Fading Markov Random Evolution

We introduce the notion of fading Markov random evolution and study the properties and characteristics of this process.     

Unbounded self-adjoint operators connected by algebraic relations

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 12, pp.1664–1668, December, 1989.