Local Rigidity for Symplectic Billiards

Key Points

• Local rigidity demonstrates that if a domain is nearly an ellipse, it must be an ellipse for integrability.
• The proof involves rational integrability and highlights important geometric properties in symplectic dynamics.
• This analysis builds on previous results regarding Birkhoff billiards, expanding the understanding of billiard systems.
• The implications suggest limited class traits for integrable symplectic billiards based on domain shapes.