Ernesto Perez-Chavela - Heteroclinic phenomena in the Sitnikov problem

We give the deduction of a Melnikov function for the Sitnikov problem. Using a perturbation method introduced by Melnikov and a thorough analysis of the geometry of certain auxiliary functions that we introduce, we prove analytically the existence of transverse heteroclinic orbits. As a consequence, we can embed a Bernoulli shift near these orbits, showing that the Sitnikov problem possesses chaotic dynamics.