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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 096, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.096
(Mi sigma1077)
 

This article is cited in 7 scientific papers (total in 7 papers)

Harmonic Oscillator on the $\mathrm{SO}(2,2)$ Hyperboloid

Davit R. Petrosyana, George S. Pogosyanbc

a Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region, 141980, Russia
b Departamento de Matematicas, CUCEI, Universidad de Guadalajara, Guadalajara, Jalisco, Mexico
c International Center for Advanced Studies, Yerevan State University, A. Manoogian 1, Yerevan, 0025, Armenia
References:
Abstract: In the present work the classical problem of harmonic oscillator in the hyperbolic space $H_2^2$: $z_0^2+z_1^2-z_2^2-z_3^2=R^2$ has been completely solved in framework of Hamilton–Jacobi equation. We have shown that the harmonic oscillator on $H_2^2$, 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.
Keywords: superintegrable systems; harmonic oscillator; hyperbolic space; Hamilton–Jacobi equation.
Received: April 24, 2015; in final form November 20, 2015; Published online November 25, 2015
Bibliographic databases:
Document Type: Article
Language: English
Citation: Davit R. Petrosyan, George S. Pogosyan, “Harmonic Oscillator on the $\mathrm{SO}(2,2)$ Hyperboloid”, SIGMA, 11 (2015), 096, 23 pp.
Citation in format AMSBIB
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\by Davit~R.~Petrosyan, George~S.~Pogosyan
\paper Harmonic Oscillator on the $\mathrm{SO}(2,2)$ Hyperboloid
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\vol 11
\papernumber 096
\totalpages 23
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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