Conewise Linear Periodic Maps of the Plane with Integer Coefficients

Abstract

We study periodic, conewise linear maps of the plane with integer coefficients starting with Mort Brown's map. We show that if the number of cones 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 cones, a map can have any period. We show how to construct such maps using binary trees and so called admissible sequences.

Additional information

Notes on contributors

Grant Cairns

GRANT CAIRNS studied electrical engineering at the University of Queensland, Australia, and then differential geometry under Pierre Molino at USTL Montpellier, France. He has taught at La Trobe University since 1988.

Yuri Nikolayevsky

YURI NIKOLAYEVSKY received his Ph.D. in 1990 at Kharkov University, USSR, under Alexander Borisenko. He has taught at La Trobe University since 2004.

Gavin Rossiter

GAVIN ROSSITER was a student at La Trobe University at the time this paper was written. This work originated from Gavin's Summer Research Scholarship supervised by the first two authors. Gavin is currently studying computer science.