Fractional Hamiltonian monodromy from a Gauss–Manin monodromy

Dominique Sugny (1) , Pavao Mardesic (2) , Michèle Pelletier (2) , Ahmad Jebrane (2) , Hans-Rudolf Jauslin (1)

1 ICB - Laboratoire Interdisciplinaire Carnot de Bourgogne
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by Nekhoroshev, Sadovskií, and Zhilinskií, C. R. Acad. Sci. Paris, Ser. 1 335, 985 2002; 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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Dominique Sugny, Pavao Mardesic, Michèle Pelletier, Ahmad Jebrane, Hans-Rudolf Jauslin. Fractional Hamiltonian monodromy from a Gauss–Manin monodromy. Journal of Mathematical Physics, 2008, 49, pp.042701. ⟨10.1063/1.2863614⟩. ⟨hal-00508382⟩