Sets of all periodic points of a toral automorphism

Abstract

In this article, subsets of ${\mathbb{T}}^2$ that can arise as sets of all periodic points of a continuous 2-dimensional toral automorphism are characterized. Here the torus ${\mathbb{T}}^2$ is viewed as $[0,1)\times [0,1)$ as a group under coordinatewise addition modulo 1.