Separatrix connection and chaotic dynamics in the Hess-Appeltot case

We consider a special situation of the Hess-Appelrot case of the Euler-Poisson system which describes the dynamics of a rigid body about a fixed point. One has an equilibrium point of saddle type with coinciding stable and unstable invariant 2-dimensional manifolds. We show rigorously that, after a generic perturbation of the Hess-Appelrot case, the invariant manifolds are split such that only finite number of 1-dimensional homoclinic trajectories remain and that such situation leads to a chaotic dynamics with positive entropy and to non-existence of any additional first integral.