Break-up of invariant curves in the Fermi-Ulam model

Abstract

The transport of particles in the phase space is investigated in the Fermi-Ulam model. The system consists of a particle confined to move within two rigid walls with which it collides. One is fixed and the other is periodically moving in time. In this work we investigate, for this model, the location of invariant curves that separate chaotic areas in the phase space. Applying the Slater's theorem we verify that the mapping presents a family of invariant spanning curves with a rotation number whose expansion into continued fractions has an infinite tail of the unity, acting as local transport barriers. We study the destruction of such curves and find the critical parameters for that. The determination of the rotation number in the vicinity of one of the considered spanning curves allowed us to understand the dynamics in the vicinity of the considered curve, both before and after criticality. The rotation number profile showed us the fractal character of the region close to the curve, since this profile has a structure similar to a “Devil's Staircase”.