Some tastings in Morales-Ramis theory

Abstract

In this paper we present a short material concerning to some results in Morales-Ramis theory, which relates two different notions of integrability: Integrability of Hamiltonian systems through Liouville Arnold theorem and integrability of linear differential equations through differential Galois theory. As contribution, we obtain the abelian differential Galois group of the variational equation related to a bi-parametric Hamiltonian system.