Ergodic billiards that are not quantum unique ergodic
Partially rectangular domains are compact two-dimensional Riemannian manifolds X, either closed or with boundary, that contain a flat rectangle or cylinder. In this paper we are interested in partially rectangular domains with ergodic billiard flow; examples are the Bunimovich stadium, the Sinai billiard or Donnelly surfaces. We consider a one-parameter family Xt of such domains parametrized by the aspect ratio t of their rectangular part. There is convincing theoretical and numerical evidence...[Show more]
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