Deceleration mechanism of Fermi acceleration in a time-dependent stadium   billiard
  The dynamics of a time-dependent stadium-like billiard are studied by a four dimensional nonlinear mapping. We have shown that even without any dissipation, the particle experiences a decrease on its velocity. Such condition is related with a critical resonance velocity, where if the initial velocity has a higher value than the resonant one, we can observe Fermi acceleration, however, if the initial velocity has a initial value smaller than the critical one, the particle is temporarily trapped surrounding the stability islands, in a stickiness regime. We believe that this sticky orbits can act as deceleration mechanism for Fermi Acceleration. 
Andr\'e L. P. Livorati, Alexander Loskutov and Edson D. Leonel
nlin.CD