Dissipation in the Fermi-Ulam Model

Abstract

We discuss in this chapter some dynamical properties for the Fermi-Ulam model under different dissipative forces. The first type considered is through inelastic collisions that is when the particle has a fractional loss of energy upon collision. We will show that depending on the control parameters, stable and unstable manifolds obtained from the same saddle fixed point cross each other producing a crisis event. Such a crisis destroys the chaotic attractor which is replaced by a chaotic transient. Another type of dissipative force is when the particle crosses a viscous media hence losing energy along its trajectory. Three different types of drag forces will be considered: (i) proportional to the velocity of the particle; (2) proportional to square of the velocity and; (3) proportional to a power of the velocity different from the linear and from the quadratic.