Fermi acceleration and scaling properties of a time dependent oval billiard

We consider the phenomenon of Fermi acceleration for a classical particle inside an area with a closed boundary of oval shape. The boundary is considered to be periodically time varying and collisions of the particle with the boundary are assumed to be elastic. It is shown that the breathing geometry causes the particle to experience Fermi acceleration with a growing exponent rather smaller as compared to the no breathing case. Some dynamical properties of the particle's velocity are discussed in the framework of scaling analysis.