Christophe Leuridan

Linear toral endomorphisms, exactness, Bernoulliness and generators

Let $T$ be a non-invertible surjective continuous endomorphism of the group $\ttf^d\,:= \rrf^d/\zzf^d$. Then $T$ preserves the Haar measure, is associated to some $d \times d$ matrix $A$ with integer coefficients and is $r$-to-one, where $r = |\det A| \ge 2$. In~\cite{Krzyzewski}, Krzy\.{z}ewski gives a necessary and s...