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Communications in Mathematical Physics

, Volume 175, Issue 3, pp 673–682 | Cite as

Ergodicity of eigenfunctions for ergodic billiards

  • Steven Zelditch
  • Maciej Zworski
Article

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.

Keywords

Boundary Condition Neural Network Manifold Statistical Physic Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Steven Zelditch
    • 1
  • Maciej Zworski
    • 1
  1. 1.Mathematics DepartmentJohns Hopkins UniversityBaltimoreUSA

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