Local rigidity for symplectic billiards

2025/01/15 by Tsodikovich, Daniel · 2 citations
#37C05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.08849

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.

Cited by

• Birkhoff attractors for dissipative symplectic billiards
• Isoperimetric-type inequalities for Mather's β-function of convex billiards

Related

• Totally integrable symplectic billiards are ellipses
• Deformational spectral rigidity of axially-symmetric symplectic billiards
• Bialy-Mironov type rigidity for centrally symmetric symplectic billiards
• Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse
• Bialy-Mironov type rigidity for centrally symmetric symplectic billiards