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Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application

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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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Authors and Affiliations

  1. Moscow State Institute for Electronics and Mathematics (, Moscow Technical University, Moscow, Russia

    V. V. Belov & V. A. Maksimov

  2. Institute for Problems in Mechanics, RAS, Moscow, Russia

    S. Yu. Dobrokhotov

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  1. V. V. Belov
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  2. S. Yu. Dobrokhotov
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  3. V. A. Maksimov
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Belov, V.V., Dobrokhotov, S.Y. & Maksimov, V.A. Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application. Theoretical and Mathematical Physics 135, 765–791 (2003). https://doi.org/10.1023/A:1024022718890

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