An Investigation of the Chaotic Transient for a Boundary Crisis in the Fermi-Ulam Model
Investigation of some statistical properties for a chaotic transient in a Fermi-Ulam model observed after a boundary crisis is considered in this chapter. The crisis is produced by a crossing of a stable and unstable manifold generated from the same saddle fixed point, hence creating also a homoclinic crossing. The system consists of a classical particle bouncing between two rigid and infinitely heavy walls. One of them is fixed while the other one is moving periodically in time. The dynamics of the system is given by a two-dimensional, nonlinear area-contracting map for the variables velocity of the particle immediately after a collision with the moving wall and time after such a collision. The collisions are assumed to be inelastic, hence a fractional loss of energy is observed leading to the existence of attractors in the phase space.
EDL acknowledges the support from CNPq (303707/2015-1), FAPESP (2017/14414-2), and FUNDUNESP. MFM thanks to CNPq and CAPES for support.
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