English

Examples of reflective projective billiards and outer ghost billiards

Dynamical Systems 2020-04-14 v2

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 22-parameters family of nn-periodic orbits, with nn being either 33 or any even number grower than 44.

Keywords

Cite

@article{arxiv.2002.09845,
  title  = {Examples of reflective projective billiards and outer ghost billiards},
  author = {Corentin Fierobe},
  journal= {arXiv preprint arXiv:2002.09845},
  year   = {2020}
}
R2 v1 2026-06-23T13:50:39.527Z