English

Outer billiards

Dynamical Systems 2017-11-27 v3

Abstract

In this paper outer, or dual, billiards outside regular polygons are studied; in particular, periodic points for cases of strictly convex "tables" and for regular n-gons with n = 3,4,6,8,12 are discussed. The main results of the paper are: 1) proof of an existence of aperiodic points for outer billiards outside regular octagon and dodecagon; 2) proof of the fact that for regular octagon, set of periodic points is of full measure; 3) list of all possible periods for case of regular octagon.

Keywords

Cite

@article{arxiv.1505.06332,
  title  = {Outer billiards},
  author = {Filipp Rukhovich},
  journal= {arXiv preprint arXiv:1505.06332},
  year   = {2017}
}

Comments

60 pages; Russian language

R2 v1 2026-06-22T09:40:09.373Z