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Chaotic scattering and acceleration of particles by waves.

Relativistic charged particles in a uniform magnetic field and traveling waves of large amplitude can be accelerated limitlessly. Since much of phase space is chaotic the process can be viewed as chaotic scattering on waves. For multiple waves an explicit map arises with unusual properties. It contains infinite island chains around nonperiodic orbits and it is also an example of transient chaos in a Hamiltonian system.