Constant slope models for finitely generated maps (Q1661079)

It is well known that a piecewise monotone topologically mixing map \(f:[0,1] \rightarrow [0,1]\) is topologically conjugate to a unique constant slope map \(T\) and that the slope of \(T\) is \(\exp (h(f))\), where \(h(f)\) denotes the topological entropy of \(f\). The paper under review generalizes this result to the class of finitely generated maps, which are countably monotone. The author proves that a finitely generated map \(g\) is topologically conjugate to at most one constant slope map \(T\) and that the slope of \(T\) is \(\exp (h(g))\) if \(T\) exists. He shows that \(T\) exists if and only if \(g\) is Vere-Jones recurrent.