Fractional Hamiltonian monodromy from a Gauss–Manin monodromy

D. Sugny, P. Mardešić, M. Pelletier, A. Jebrane, H. R. Jauslin
2008 Journal of Mathematical Physics  
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
more » ... of singularities. We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n and m:-n resonant systems.
doi:10.1063/1.2863614 fatcat:asjfvtaffvc5bd7k5udzdwhu6u