Ergodicity of eigenfunctions for ergodic billiards

Steven Zelditch; Maciej Zworski

doi:10.1007/BF02099513

Ergodicity of eigenfunctions for ergodic billiards

Steven Zelditch^*, Maciej Zworski

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

127 Scopus citations

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.

Original language	English (US)
Pages (from-to)	673-682
Number of pages	10
Journal	Communications in Mathematical Physics
Volume	175
Issue number	3
DOIs	https://doi.org/10.1007/BF02099513
State	Published - 1996

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02099513

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title = "Ergodicity of eigenfunctions for ergodic billiards",

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.",

author = "Steven Zelditch and Maciej Zworski",

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journal = "Communications in Mathematical Physics",

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T1 - Ergodicity of eigenfunctions for ergodic billiards

AU - Zelditch, Steven

AU - Zworski, Maciej

PY - 1996

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AB - 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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U2 - 10.1007/BF02099513

DO - 10.1007/BF02099513

M3 - Article

AN - SCOPUS:0030530411

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Ergodicity of eigenfunctions for ergodic billiards

Abstract

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