# Liouville integrability: an effective Morales-Ramis-Simo theorem

##
Thomas Dreyfus

created by daniele on 27 May 2015

28 may 2015
-- 14:00

Sala Conferenze, Collegio Puteano, Pisa

Seminari di Dinamica Olomorfa, Pisa

**Abstract.**

Morales-Ramis theorem roughly states as follows: Given an
Hamiltonian system, we may linearize it to obtain the variational
equation. Then, we associate to the variational equation a group, the
differential Galois group. Morales and Ramis have proved that if the
Hamiltonian system is integrable in a certain sense, then the Galois group
has a certain algebraic property. This theorem has been
generalized by Morales-Ramis-Simo. In this talk, we will explain how to
check effectively whether the algebraic property of the Galois group is
satisfied or not.