On the dynamical properties of an elliptical–oval billiard with static boundary

Some dynamical properties for a classical particle confined inside a closed region with an elliptical–oval-like shape are studied. The dynamics of the model is made by using a two-dimensional nonlinear mapping. The phase space of the system is of mixed kind and we have found the condition that breaks the invariant spanning curves in the phase space. We have discussed also some statistical properties of the phase space and obtained the behaviour of the positive Lyapunov exponent.