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.     

Investigation of the ηη system in π − p interactions at a momentum of 32.5 GeV/c at the GAMS-4π spectrometer

The ηη system produced in charge-exchange π ^? p interaction at a momentum of 32.5 GeV/c is studied in an experiment performed with the GAMS-4π spectrometer at the 70-GeV accelerator of the Institute for High-Energy Physics (IHEP, Protvino). A partial-wave analysis is performed in the mass range between 1.1 and 3.9 GeV for ?t <0.2 (GeV/c)², S, D, G, and J waves being taken into account in this analysis. The S wave has a complicated structure, displaying peaks at about 1.5 and 1.7 GeV. These peaks are associated with the f ₀(1500) and f ₀(1710) mesons. One of the solutions (preferable one) involves the f ₀(2200) and f ₂(1950) resonances. The mass region above 2.4 GeV is dominated by the G wave. A broad state of mass about 3 GeV and width 0.7 GeV is found in the J wave. The parameters of the resonances in question and their production cross sections are measured.     

Dynamics of conflict interaction between systems with internal structure

We investigate a dynamical system of conflict between two systems each of which, in turn, has an internal conflict. The external conflict and the internal one have different natures. The external conflict is described by an alternative interaction between nonannihilating adversaries. The internal conflict is similar to a conflict between interrelated populations of different biological nature (“predator-prey” model). We construct a computer model of this system and describe a typical behavior, illustrated by diagrams, which can be interpreted, in particular, as a migration of labor and investments between countries. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 4, pp. 435–450, October–December, 2006.