Non-Hamiltonian monochromy

Abstract

It has been proved by Maorong Zou and Nguyen Tien Zung that nontrivial monodromy occurs in every integrable two degrees of freedom Hamiltonian system which has a proper momentum mapping with a focusfocus singularity In this paper we describe a generalization of this result which does not use the Hamiltonian structure of the system This can be used to prove that nontrivial monodromy occurs in the two best known integrable cases of rolling bodies the heavy solid of revolution rolling on a horizontal plane and the sphere rolling in a circular bowl with an upward dimple at the bottom