Geodesic
Explicit Formulas for Generalized Action--Angle Variables in a Neighborhood of an Isotropic Torus and Their Application
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 378-408

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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.
Keywords: isotropic tori, semiclassical asymptotic approximations.
Mots-clés : action–angle variables 
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     author = {V. V. Belov and S. Yu. Dobrokhotov and V. A. Maksimov},
     title = {Explicit {Formulas} for {Generalized} {Action--Angle} {Variables} in a {Neighborhood} of an {Isotropic} {Torus} and {Their} {Application}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {378--408},
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     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a2/}
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V. V. Belov; S. Yu. Dobrokhotov; V. A. Maksimov. Explicit Formulas for Generalized Action--Angle Variables in a Neighborhood of an Isotropic Torus and Their Application. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 378-408. http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a2/