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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162326We 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 pagesDynamical Systems37E05, 37B10, 11B34, 37B40Computation of Topological Entropy via $ϕ$-expansion, an Inverse Problem for the Dynamical Systems $βx+α\mod 1$text