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Ergodicity of eigenfunctions for ergodic billiards. (English) Zbl 0840.58048
Summary: 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.

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
37A99 Ergodic theory
Full Text: DOI
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