# Fermi acceleration and adiabatic invariants for non-autonomous billiards.

@article{Gelfreich2012FermiAA, title={Fermi acceleration and adiabatic invariants for non-autonomous billiards.}, author={V. Gelfreich and Vered Rom-Kedar and Dmitry Turaev}, journal={Chaos}, year={2012}, volume={22 3}, pages={ 033116 } }

Recent results concerned with the energy growth of particles inside a container with slowly moving walls are summarized, augmented, and discussed. For breathing bounded domains with smooth boundaries, it is proved that for all initial conditions the acceleration is at most exponential. Anosov-Kasuga averaging theory is reviewed in the application to the non-autonomous billiards, and the results are corroborated by numerical simulations. A stochastic description is proposed which implies that…

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