A note on the semiclassical measure at singular points of the boundary of the Bunimovich stadium
Mangoubi, Dan1; Weller Weiser, Adi1
1 Einstein Institute of Mathematics Edmond J. Safra campus The Hebrew University of Jerusalem Jerusalem 9190401 (Israel)
Annales de l'Institut Fourier, Online first, 9 p.

An argument by Hassell proving the existence of a Bunimovich stadium for which there are semiclassical measures giving positive mass to the submanifold of bouncing ball trajectories uses a notion of non-gliding points. However, this notion is defined only for domains with C 2 -boundaries. The purpose of this note is to clarify the argument.

Un argument de Hassell montrant l’existence d’un stade de Bunimovich sur lequel on trouve une mesure semiclassique chargeant la sous-variété des trajectoires de boules rebondissantes fait appel à la notion de points non-gliding. Pourtant, cette notion suppose un domaine lisse C 2 . Le but de cette note est de clarifier ce point.

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Accepted:
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DOI: 10.5802/aif.3601
Classification: 58J51, 37D50, 81Q50
Keywords: Bunimovich’s stadium, quantum unique ergodicity, non-smooth boundary, non-gliding
Mot clés : stade de Bunimovich, unique ergodicité quantique, bord non-lisse, non-gliding
Mangoubi, Dan 1; Weller Weiser, Adi 1

1 Einstein Institute of Mathematics Edmond J. Safra campus The Hebrew University of Jerusalem Jerusalem 9190401 (Israel) 
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Mangoubi, Dan; Weller Weiser, Adi. A note on the semiclassical measure at singular points of the boundary of the Bunimovich stadium. Annales de l'Institut Fourier, Online first, 9 p.

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