Numerical study on ergodic properties of triangular billiards

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Abstract
We consider the motion of a point particle in right triangular billiards. By considering the global dynamics (when acute angles are not rationally connected to π), or the discrete reduced dynamics (when acute angles are rational multiples of π), we find numerical evidence for the conjecture that the motion is ergodic and weakly mixing. These dynamical features are intimately related to nontrivial scaling properties of the spectrum of the evolution operator.