Fractional Hamiltonian monodromy from a Gauss-Manin monodromy

Journal Article · Tue Apr 15 00:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2863614· OSTI ID:21100260

Sugny, D; Jauslin, H R ^[1]; Mardesic, P; Pelletier, M; Jebrane, A ^[2]

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1. Institut Carnot de Bourgogne, UMR 5209 CNRS-Universite de Bourgogne, BP 47870, 21078 Dijon (France)
2. Institut de Mathematiques de Bourgogne, UMR CNRS 5584, BP 47870, 21078 Dijon (France)

Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskii, and Zhilinskii, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); and Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m:-n resonant systems.

• OSTI ID: 21100260
• Journal Information: Journal of Mathematical Physics, Vol. 49, Issue 4; Other Information: DOI: 10.1063/1.2863614; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BIFURCATION
GEOMETRY
HAMILTONIANS
MAPS
MATHEMATICAL SPACE
MATRICES
RIEMANN SHEET
SINGULARITY