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arXiv · 0709.2765

Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy

D. Sugny·P. Mardesic·M. Pelletier·A. Jebrane·H. R. Jauslin
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Abstract

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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D. Sugny, P. Mardesic, M. Pelletier, A. Jebrane, H. R. Jauslin. 2007-09-18. Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy. https://doi.org/10.1063/1.2863614

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