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Local rigidity for symplectic billiards (2501.08849v1)
Published 15 Jan 2025 in math.DS
Abstract: We show a local rigidity result for the integrability of symplectic billiards. We prove that any domain which is close to an ellipse, and for which the symplectic billiard map is rationally integrable must be an ellipse as well. This is in spirit of the result of Avila, De Simoi, and Kaloshin for Birkhoff billiards.
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