English

Scarcity of periodic orbits in outer billiards

Dynamical Systems 2017-12-27 v2

Abstract

We give a simple proof of our previous result with V. Zharnitsky that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior, provided that no four corners of the boundary form a parallelogram. We also obtain results on period 5 and 6 orbits.

Keywords

Cite

@article{arxiv.1706.03882,
  title  = {Scarcity of periodic orbits in outer billiards},
  author = {Alexander Tumanov},
  journal= {arXiv preprint arXiv:1706.03882},
  year   = {2017}
}

Comments

12 pages, minor typos corrected