Taylor obstruction to the integrability of homogeneous potentials of degree two. An application of higher order variational equations
Banach Center Publications 94 (2011), 173-185 MSC: 70Hxx, 37J30. DOI: 10.4064/bc94-0-10
We show how using the differential Galois theory one can find effectively necessary conditions for the integrability of Hamiltonian systems with homogeneous potentials.