【摘 要】
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In this paper,we introduce a new notion of integrability for billiard tables,namely,inte-grability away from the boundary.One key feature of our notion is that the integrable region could be disjoint from the boundary with a positive distance.We prove tha
【机 构】
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Yau Mathematical Sciences Center,Tsinghua University,Beijing 100084,P.R.China
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In this paper,we introduce a new notion of integrability for billiard tables,namely,inte-grability away from the boundary.One key feature of our notion is that the integrable region could be disjoint from the boundary with a positive distance.We prove that if a strictly convex billiard table,whose boundary is a small perturbation of an ellipse with small eccentricity,is integrable in this sense,then its boundary must be itself an ellipse.
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