The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos
The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos
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 separatrices. We show rigorously that, after a suitable perturbation of …