Dynamics Seminar

Date: Monday, April 19, 2010.
Room and time: Groningen, Zernike Campus, Bernoulliborg 5161.0293, 14:00.

Konstantinos Efstathiou

University of Groningen

Uncovering fractional monodromy

Abstract

Fractional monodromy has been introduced recently in the study of Liouville integrable Hamiltonian systems as a characteristic property of the geometry of their fibration. Unlike standard monodromy, fractional monodromy takes into account the singular fibres of the system. In this talk I prove fractional monodromy for m:(-n) resonant Hamiltonian systems with m, n coprime natural numbers. The geometry of the fibration is simplified by passing to an appropriate covering space. Pushing the results of the parallel transport of homology cycles in the covering space down to the original space gives fractional monodromy. I give a very detailed description of the geometry of the fibres both in the original and in the covering spaces and discuss a generalization of the notion of parallel transport of homology cycles.

The talk is based on a joint work with Henk Broer.