Problem dossier · Dynamics & Analysis
Birkhoff conjecture on integrable billiards
If the billiard dynamics inside a smooth convex curve is integrable (foliated by caustics), the curve must be an ellipse.
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Status
Open in full; proved for perturbations of ellipses (Avila–De Simoi–Kaloshin, Kaloshin–Sorrentino local versions).
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The Angle of Attack
Numerically test integrability breakdown for perturbed ellipses and near-elliptical ovals; measure caustic destruction rates against the local theorems.
Tags: billiards · integrability · caustics · perturbation
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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