Orbit Representations from Linear mod 1 Transformations

Carlos Correia Ramos, Nuno Martins, Paulo R. Pinto

We show that every point $x_0\in [0,1]$ carries a representation of a $C^{\ast }$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{\beta ,\alpha }(x)=\beta x+\alpha$. Such $C^{\ast }$…