Period sets of linear toral endomorphisms on $T^2$

Abstract

The period set of a dynamical system is defined as the subset of all integers $n$ such that the system has a periodic orbit of length $n$. Based on known results on the intersection of period sets of torus maps within a homotopy class, we give a complete classification of the period sets of (not necessarily invertible) toral endomorphisms on the $2$--dimensional torus $\mathbb{T}^2$.