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We calculated the classical electron dynamics of three-dimensional electrons in a billiard system in tilted magnetic field and analyzed the evolution of trajectories in phase space by means of Poincare space of sections. The low field magnetoresistance rxx was calculated through linear response theory and found that nonlinear resonances between the cyclotron radius Rc, the antidot lattice period a, and the well width W, are reflected in the observed magnetoresistance peaks.

Evolution from commensurability to size-effects structures in three-dimensional billiards