Harmonic Oscillator on the SO(2,2) Hyperboloid
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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2015 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2015
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147158 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734348757762048 |
|---|---|
| author | Petrosyan, D.R. Pogosyan, G.S. |
| author_facet | Petrosyan, D.R. Pogosyan, G.S. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T19:42:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147158 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:42:45Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Petrosyan, D.R. Pogosyan, G.S. 2019-02-13T17:51:31Z 2019-02-13T17:51:31Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147158 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Harmonic Oscillator on the SO(2,2) Hyperboloid Article published earlier |
| spellingShingle | Harmonic Oscillator on the SO(2,2) Hyperboloid Petrosyan, D.R. Pogosyan, G.S. |
| title | Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_full | Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_fullStr | Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_full_unstemmed | Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_short | Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_sort | harmonic oscillator on the so(2,2) hyperboloid |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147158 |
| work_keys_str_mv | AT petrosyandr harmonicoscillatorontheso22hyperboloid AT pogosyangs harmonicoscillatorontheso22hyperboloid |