A simple proof of the geometric fractional monodromy theorem
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J. J. Duistermaat “On Global Action Angle Coordinates”, Communs. Pure and Appl. Math. 33, 687 (1980).
K. Efstathiou, Metamorphoses of Hamiltonian Systems with Symmetries (Lect. Notes Math., Springer-Verlag, Berlin, Heidelberg, 2005).
N. Nekhoroshev, D. Sadovskii, and B. Zhilinskii, “Fractional Hamiltonian Monodromy,” Ann. Henri Poincaré 7, 1099 (2006).
N. Nekhoroshev, “Fractional Monodromy in the Case of Arbitrary Resonances,” Matem. Sbornik 198(3), 91 (2007) [Sbornik Math. 198 (3), 383 (2007)].
D. Sadovskii and B. Zhilinskii, “Quantum Monodromy, its Generalizations and Molecular Manifestations” Mol. Phys. 104, 2595 (2006).
H. Broer, K. Efstathiou, and O. Lukina, “A Geometric Fractional Monodromy Theorem” Discrete and Continuous Dynamical Systems 3(4), 517 (2010).
A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems. Geometry, Topology, Classification (Chapman and Hall/CRC, Boca Raton, Florida, 2004).
A. T. Fomenko, “Morse Theory of Integrable Hamiltonian Systems,” Doklady Akad. Nauk SSSR 287(5), 1071 (1986) [Soviet Math. Dokl. 33 (2), 502 (1986)].
A. T. Fomenko, “The Topology of Surfaces of Constant Energy in Integrable Hamiltonian Systems, and Obstructions to Integrability,” Izv. Akad. Nauk SSSR, Ser. Matem. 50(6), 1276 (1986) [Math, of the USSR — Izvestiya 29 (3), 629 (1987)].
A. T. Fomenko and H. Zieschang, “On Typical Topological Properties of Integrable Hamiltonian Systems,” Izv. Akad. Nauk SSSR, Ser. Matem. 52(2), 378 (1988) [Math, of the USSR — Izvestiya 32 (2), 385 (1989)].