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2013
Impact Factor

Oleg Zubelevich

Leninskie gory 1, Moscow, 119991, Russia
Lomonosov Moscow State University

Publications:

Zubelevich O. E.
A note on theorem of Massera
2006, vol. 11, no. 4, pp.  475-481
Abstract
In this paper we consider a discrete dynamical system generated by bounded affine mappings on Banach spaces and on Montel locally convex spaces. We show that if these dynamical systems have bounded trajectories then they have periodic ones. Different applications are considered.
Keywords: Massera criterion, periodic solution, dynamical systems
Citation: Zubelevich O. E.,  A note on theorem of Massera , Regular and Chaotic Dynamics, 2006, vol. 11, no. 4, pp. 475-481
DOI: 10.1070/RD2006v011n04ABEH000365
Zubelevich O. E.
On Exponentially Small Effects in Dynamical Systems with a Small Parameter
2002, vol. 7, no. 3, pp.  315-324
Abstract
In the present paper we obtain a theorem which enables us to treat different exponentially small effects of dynamics from a unified point of view. As an example, we discuss the problem of fast phase averaging in multi-frequency systems with slow variable belonging to Banach space.
Citation: Zubelevich O. E.,  On Exponentially Small Effects in Dynamical Systems with a Small Parameter, Regular and Chaotic Dynamics, 2002, vol. 7, no. 3, pp. 315-324
DOI:10.1070/RD2002v007n03ABEH000213
Treschev D. V., Zubelevich O. E.
Invariant tori in Hamiltonian systems with two degrees of freedom in a neighborhood of a resonance
1998, vol. 3, no. 3, pp.  73-81
Abstract
An estimate for the difference of the frequencies on two invariant curves, bounding a resonance zone of an area-preserving close to integrable map, is obtained. Analogous results for Hamiltonian systems are presented.
Citation: Treschev D. V., Zubelevich O. E.,  Invariant tori in Hamiltonian systems with two degrees of freedom in a neighborhood of a resonance, Regular and Chaotic Dynamics, 1998, vol. 3, no. 3, pp. 73-81
DOI:10.1070/RD1998v003n03ABEH000081

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