Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

► The system is described via a two-dimensional nonlinear area-contracting map. ► Dissipation destroys the mixed phase space structure and attractors appear. ► After a small change in the dissipation parameter a boundary crisis occurs. ► The chaotic transient is described by a power law with exponent −2. ► The parameter space presents infinite self-similar structures of shrimp-shape.