Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application |
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Authors: | Belov V V Dobrokhotov S Yu Maksimov V A |
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Institution: | (1) Moscow State Institute for Electronics and Mathematics (, Moscow Technical University, Moscow, Russia;(2) Institute for Problems in Mechanics, RAS, Moscow, Russia |
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Abstract: | Different versions of the Darboux–Weinstein theorem guarantee the existence of action–angle-type variables and the harmonic-oscillator variables in a neighborhood of isotropic tori in the phase space. The procedure for constructing these variables is reduced to solving a rather complicated system of partial differential equations. We show that this system can be integrated in quadratures, which permits reducing the problem of constructing these variables to solving a system of quadratic equations. We discuss several applications of this purely geometric fact in problems of classical and quantum mechanics. |
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Keywords: | isotropic tori action– angle variables semiclassical asymptotic approximations |
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