The Fermi-Ulam Accelerator Model Under Scaling Analysis
  The chaotic low energy region of the Fermi-Ulam simplified accelerator model is characterised by use of scaling analysis. It is shown that the average velocity and the roughness (variance of the average velocity) obey scaling functions with the same characteristic exponents. The formalism is widely applicable, including to billiards and to other chaotic systems. 
Edson D. Leonel, P.V.E.McClintock and J. Kamphorst Leal da Silva