On Combinatorial Types of Periodic Orbits of the Map $x\mapsto kx$ (mod $\mathbb{Z}$)

Carsten L. Petersen, Saeed Zakeri

We study the combinatorial types of periodic orbits of the standard covering endomorphisms ${\mathbf{m}}_k(x)=kx(\text{mod}\mathbb{Z})$ of the circle for integers $k\ge 2$…