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<p>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 [<CitationRef CitationID="CR2">2</CitationRef>] for Birkhoff billiards.</p>

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Local Rigidity for Symplectic Billiards

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月7日

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  • Daniel Tsodikovich

摘要

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 [2] for Birkhoff billiards.