Abstract
We give a simple proof of ergodicity of eigenfunctions of the Laplacian with Dirichlet boundary conditions on compact Riemannian manifolds with piecewise smooth boundaries and ergodic billiards. Examples include the “Bunimovich stadium”, the “Sinai billiard” and the generic polygonal billiard tables of Kerckhoff, Masur and Smillie.
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Communicated by Ya.G. Sinai
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Zelditch, S., Zworski, M. Ergodicity of eigenfunctions for ergodic billiards. Commun.Math. Phys. 175, 673–682 (1996). https://doi.org/10.1007/BF02099513
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DOI: https://doi.org/10.1007/BF02099513