Phase transition on Exel crossed products assocaited to dilation matrices

Marcelo Laca, Iain Raeburn, Jacqui Ramagge

An integer matrix $A\in M_d(\mathbb{Z})$ induces a covering ${\sigma }_A$ of $\T^d$ and an endomorphism ${\alpha }_A:f\mapsto f\circ {\sigma }_A$ of $C(\T^d)$ for which there is a natural transfer operator $L$. I…