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Harmonic Oscillator on the SO(2,2) Hyperboloid
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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| dc.contributor.author | Petrosyan, D.R. | |
| dc.contributor.author | Pogosyan, G.S. | |
| dc.date.accessioned | 2019-02-13T17:51:31Z | |
| dc.date.available | 2019-02-13T17:51:31Z | |
| dc.date.issued | 2015 | |
| dc.identifier.citation | Harmonic Oscillator on the SO(2,2) Hyperboloid / D.R. Petrosyan, G.S. Pogosyan // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 22E60; 37J15; 37J50; 70H20 | |
| dc.identifier.other | DOI:10.3842/SIGMA.2015.096 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/147158 | |
| dc.description.abstract | In the present work the classical problem of harmonic oscillator in the hyperbolic space H²₂: z²₀+z²₁−z²₂−z²₃=R² has been completely solved in framework of Hamilton-Jacobi equation. We have shown that the harmonic oscillator on H²₂, as in the other spaces with constant curvature, is exactly solvable and belongs to the class of maximally superintegrable system. We have proved that all the bounded classical trajectories are closed and periodic. The orbits of motion are ellipses or circles for bounded motion and ultraellipses or equidistant curve for infinite ones. | uk_UA |
| dc.description.sponsorship | This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html. The work of G.P. was partially supported under the Armenian-Belarus grant Nr. 13RB-035 and Armenian national grant Nr. 13-1C288. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Harmonic Oscillator on the SO(2,2) Hyperboloid | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
