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