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arXiv · 1208.2455

On Totally integrable magnetic billiards on constant curvature surface

Michael·Bialy
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Abstract

We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result is a manifestation of the so-called Hopf rigidity phenomenon which was recently obtained for classical billiards on constant curvature surfaces.

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Michael, Bialy. 2012-08-12. On Totally integrable magnetic billiards on constant curvature surface. https://arxiv.org/abs/1208.2455

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