Harmonic Oscillator on the SO(2,2) Hyperboloid
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Harmonic Oscillator on the SO(2,2) Hyperboloid
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| Creator |
Petrosyan, D.R.
Pogosyan, G.S. |
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| Description |
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.
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| Date |
2019-02-13T17:51:31Z
2019-02-13T17:51:31Z 2015 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 22E60; 37J15; 37J50; 70H20 DOI:10.3842/SIGMA.2015.096 http://dspace.nbuv.gov.ua/handle/123456789/147158 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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