Computation of Topological Entropy via $ϕ$-expansion, an Inverse Problem for the Dynamical Systems $βx+α\mod 1$

Faller, Bastien; Pfister, Charles-Edouard

Computation of Topological Entropy via $ϕ$-expansion, an Inverse Problem for the Dynamical Systems $βx+α\mod 1$

Authors

Description

We give an algorithm, based on the $ϕ$-expansion of Parry, in order to compute the topological entropy of a class of shift spaces. The idea is the solve an inverse problem for the dynamical systems $βx+α\mod1$.The first part is an exposition of the $ϕ$-expansion applied to piecewise monotone dynamical systems. We formulate for the validity of the $ϕ$-expansion, necessary and sufficient conditions, which are different from those in Parry's paper.
34 pages