Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

► In this work we consider the dynamics of a classical particle bouncing between two walls. ► One wall is fixed and the other one is described by a periodic function with two nonlinear terms. ► We investigate the rare collisions and the behaviour of saddle fixed points as a function of the control parameters. ► Scaling invariance with respect to the control parameters was observed.