Geometry of integrable non-Hamiltonian systems

TL;DR

This paper explores the geometric structure and normal forms of integrable non-Hamiltonian systems, presenting recent and original results on their local and semi-local properties and associated torus actions.

Contribution

It provides new insights and the first explicit theorems on the geometry and normal forms of integrable non-Hamiltonian systems, including systems of type (n,0).

Findings

New local and semi-local normal forms for integrable non-Hamiltonian systems

Characterization of associated torus actions

Original theorems on the geometry of systems of type (n,0)

Abstract

This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the following aspects of integrable non-Hamiltonian systems: local and semi-local normal forms and associated torus actions for integrable systems, and the geometry of integrable systems of type $(n,0)$. Most of the results presented in this text are very recent, and some theorems in this text are even original in the sense that they have not been written down explicitly elsewhere.