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Fermi acceleration in non-autonomous billiards. (English) Zbl 1139.37041

Summary: Fermi acceleration can be modelled by a classical particle moving inside a time-dependent domain and elastically reflecting from its boundary. We describe how the results from the dynamical system theory can be used to explain the existence of trajectories with unbounded energy. In particular, we show for slowly oscillating boundaries that the energy of the particle may increase exponentially fast in time.

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
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