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This article is cited in 6 scientific papers (total in 6 papers)
Global Structure and Geodesics for Koenigs Superintegrable Systems
Galliano Valent Laboratoire de Physique Mathématique de Provence,
19 bis Boulevard Emile Zola, F-13100 Aix-en-Provence, France
Abstract:
We present a new derivation of the local structure of Koenigs metrics using a
framework laid down by Matveev and Shevchishin. All of these dynamical systems allow for a
potential preserving their superintegrability (SI) and most of them are shown to be globally
defined on either $\mathbb{R}^2$ or $\mathbb{H}^2$. Their geodesic flows are easily determined thanks to their quadratic
integrals. Using Carter (or minimal) quantization, we show that the formal SI is preserved at the
quantum level and for two metrics, for which all of the geodesics are closed, it is even possible
to compute the classical action variables and the point spectrum of the quantum Hamiltonian.
Keywords:
superintegrable two-dimensional systems, analysis on manifolds, quantization.
Received: 06.08.2016 Accepted: 18.08.2016
Citation:
Galliano Valent, “Global Structure and Geodesics for Koenigs Superintegrable Systems”, Regul. Chaotic Dyn., 21:5 (2016), 477–509
Linking options:
https://www.mathnet.ru/eng/rcd199 https://www.mathnet.ru/eng/rcd/v21/i5/p477
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Abstract page: | 120 | References: | 27 |
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