Piecewise linear periodic maps of the plane with integer coefficients

2014/07/12 by Cairns, Grant, Nikolayevsky, Yuri, Rossiter, Gavin
#37C25 #37E30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.3364

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.

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