Resumen de Galosian Obstructions to Integrability of Hamiltonian Systems II

Juan José Morales Ruiz , Jean Pierre Ramis

• By applying the results of our previous paper [19], we obtain non-integrability results for the following four Hamiltonian systems: the Bianchi IX Cosmological Model, the Sitnikov system of celestial mechanics, the Spring-Pendulum system and a generalization of the homogeneous potentials considered by Yoshida. All these systems are considered over the complex domain (complex time and complex phase space) and the integrability is considered in the Liouville sense of existence of a maximal number of first integrals in involution.