Examples of reflective projective billiards and outer ghost billiards

2020/02/23 by Fierobe, Corentin
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.09845

Abstract

In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even number grower than 4.

Related

• On projective billiards with open subsets of triangular orbits
• On 4-reflective complex analytic planar billiards
• On odd-periodic orbits in complex planar billiards
• On quadrilateral orbits in complex algebraic planar billiards
• On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards