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Analytic rigidity and symbolic dynamics for two-centre billiards
We establish a sharp rigidity--chaos dichotomy for planar two-centre billiards, motivated by a natural analogue of the Birkhoff--Poritsky conjecture: the only tables integrable at every energy should be ellipses confocal with the two centres. Let $Ω$ be a bounded domain with $\mathcal C^1$ boundary
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