Geometry of Integrable non-Hamiltonian Systems

Abstract

This text is an expanded version of the lecture notes for a minicourse taught by the author at the summer school “Advanced Course on Geometry and Dynamics of Integrable Systems” organized by Vladimir Matveev, Eva Miranda and Francisco Presas at Centre de Recerca Matemàtica (CRM) Barcelona, from September 9th to 14th, 2013. The aim of this minicourse was to present some geometrical aspects of integrable non-Hamiltonian systems. Here, the adjective non-Hamiltonian does not mean that the systems in question cannot be Hamiltonian, it simply means that we consider general dynamical systems which may or may not admit a Hamiltonian structure, and even when they are Hamiltonian we can sometimes forget about their Hamiltonian nature.