Resumen de A Note on the Non-Integrability of Some Hamilitonian Systems with a Homogeneous Potential

Juan José Morales Ruiz , Jean Pierre Ramis

• We obtain a non-integrability result on Hamiltonian Systems with a homogeneous potential with an arbitrary number of degrees of freedom which generalizes a Yoshida's Theorem [7]. Except for the cases when the degree of homogeneity of the potential is equal to two or minus two, only a discrete set of families of these type of potentials are compatible with the complete integrability condition. We illustrate this result with two examples: the collinear problem of three bodies and a highly symmetrical family introduced by Umeno ([6]).