# Liouville integrability: an effective Morales-Ramis-Simo theorem – Thomas Dreyfus (Institut de Mathématiques de Toulouse)

#### Venue

Sala Conferenze (Puteano, Centro De Giorgi).

#### 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.

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