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

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

2008-06-05

arxiv.org/abs/0806.0914v1

Mathematics

Dynamical Systems

34 pages

Scientific paper

We give an algorithm, based on the $\phi$-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 $\beta x+\alpha \mod1$.The first part is an exposition of the $\phi$-expansion applied to piecewise monotone dynamical systems. We formulate for the validity of the $\phi$-expansion, necessary and sufficient conditions, which are different from those in Parry's paper.

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