Oleg Zubelevich
Publications:
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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.
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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.
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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.
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