Geodesic
Permutations of Tori in Integrable Hamiltonian Systems and Spectral Series of Pseudodifferential Operators
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 174-183

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In the present paper, we study integrable Hamiltonian systems with two degrees of freedom, whose regular level sets consist of several Liouville tori, and the bifurcation diagram has an isolated point. We study assumptions under which going around the singular point causes a permutation of the tori. We also consider a quantum analog of this situation and give model examples.
Keywords: integrable Hamiltonian system, bifurcation diagram, level set, symplectic manifold
Mots-clés : Liouville torus, quantization condition. 
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     author = {R. I. Aksitov},
     title = {Permutations of {Tori} in {Integrable} {Hamiltonian} {Systems} and {Spectral} {Series} of {Pseudodifferential} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {174--183},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a1/}
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R. I. Aksitov. Permutations of Tori in Integrable Hamiltonian Systems and Spectral Series of Pseudodifferential Operators. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 174-183. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a1/