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2013
Impact Factor

A. Itin

Moscow, 117810, Profsoyuznaya str.,84/32
Institute of Cosmic Research, RAS

Publications:

Itin A. P., Neishtadt A. I.
Resonant Phenomena in Slowly Perturbed Elliptic Billiards
2003, vol. 8, no. 1, pp.  59-66
Abstract
We consider an elliptic billiard whose shape slowly changes. During slow evolution of the billiard certain resonance conditions can be fulfilled. We study the phenomena of capture into a resonance and scattering on a resonance which lead to the destruction of the adiabatic invariance in the system.
Citation: Itin A. P., Neishtadt A. I.,  Resonant Phenomena in Slowly Perturbed Elliptic Billiards, Regular and Chaotic Dynamics, 2003, vol. 8, no. 1, pp. 59-66
DOI:10.1070/RD2003v008n01ABEH000225
Vasiliev A. A., Itin A. P., Neishtadt A. I.
On dynamics of four globally phase-coupled oscillators with close frequencies
1998, vol. 3, no. 1, pp.  9-18
Abstract
An array of four globally phase-coupled oscillators with slightly different eigenfrequencies is considered. In the case of equal frequencies the system is reduced to integrable, with almost all phase closed trajectories. In the case of different but close to each other eigenfrequencies the system is treated with the use of the averaging method. It is shown that probabilistic phenomena take place in the system: at separatrices of the unperturoed problem the phase flow splits itself quasi-randomly between various regions of the phase space. Formulas are obtained, describing probabilities of capture into various regions.
Citation: Vasiliev A. A., Itin A. P., Neishtadt A. I.,  On dynamics of four globally phase-coupled oscillators with close frequencies, Regular and Chaotic Dynamics, 1998, vol. 3, no. 1, pp. 9-18
Vasiliev A. A., Itin A. P., Neishtadt A. I.
On dynamics of four globally phase-coupled oscillators with close frequencies
1997, vol. 2, nos. 3-4, pp.  21-29
Abstract
An array of four globally phase-coupled oscillators with slightly different eigenfrequencies is considered. In the case of equal frequencies the system is reduced to an integrable one with almost all phase trajectories being closed. In the case of different but close to each other eigenfrequencies the system is treated with the use of the averaging method. It is shown that probabilistic phenomena take place in the system: the phase flow is divided quasi-randomly between various regions of the phase space when passing through separatrices of the unperturbed problem. Formulas describing probabilities of the phase point transition to different regions are obtained.
Citation: Vasiliev A. A., Itin A. P., Neishtadt A. I.,  On dynamics of four globally phase-coupled oscillators with close frequencies, Regular and Chaotic Dynamics, 1997, vol. 2, nos. 3-4, pp. 21-29
DOI:10.1070/RD1997v002n03ABEH000044

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