Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy

Details Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy

2007-09-18

arxiv.org/abs/0709.2765v1

Physics

Mathematical Physics

39 pages, 24 figures. submitted to J. Math. Phys

Scientific paper

10.1063/1.2863614

Fractional Hamiltonian Monodromy is a generalization of the notion of Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A. Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a particular type of non-isolated 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 to 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.

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