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arXiv · 0806.0914

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

Bastien Faller·Charles-Edouard Pfister
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Abstract

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.

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Bastien Faller, Charles-Edouard Pfister. 2008-06-05. Computation of Topological Entropy via $ϕ$-expansion, an Inverse Problem for the Dynamical Systems $βx+α\mod 1$. https://arxiv.org/abs/0806.0914

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