English

Piecewise linear periodic maps of the plane with integer coefficients

Dynamical Systems 2014-07-15 v1

Abstract

We study periodic, piecewise linear maps on the plane starting with the Mort Brown's map. We show that if the number of pieces is two, there is only a short list of possible periods (this fact can be seen as the crystallographic restriction for this class of maps). Otherwise, without the restriction on the number of pieces, a map can have any period. We show how to construct such maps using binary trees and so called admissible sequences.

Keywords

Cite

@article{arxiv.1407.3364,
  title  = {Piecewise linear periodic maps of the plane with integer coefficients},
  author = {Grant Cairns and Yuri Nikolayevsky and Gavin Rossiter},
  journal= {arXiv preprint arXiv:1407.3364},
  year   = {2014}
}

Comments

13 pages, 10 figures

R2 v1 2026-06-22T05:02:35.945Z