Ivrii's conjecture for some cases in outer and symplectic billiards

Abstract

We give a proof for $(2n+1,n)$ and $(2n,n-1)$-periodic Ivrii's conjecture for planar outer billiards. We also give new simple geometric proofs for the 3 and 4-periodic cases for outer and symplectic billiards, and generalize for higher dimensions in case of symplectic billiards.

10 pages, 8 figures

References in corpus (3)

• Periodic orbits in outer billiards
• On projective billiards with open subsets of triangular orbits
• Absolutely Periodic Billiard Orbits of Arbitrarily High Order