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arXiv · 1205.5902

A Combinatorial Characterization of the Critical Itineraries of a Uniform Dynamical System

Michael Barnsley·Wolfgang Steiner·Andrew Vince
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Abstract

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of $\beta$-expansions (with positive or negative $\beta$) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

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Michael Barnsley, Wolfgang Steiner, Andrew Vince. 2012-05-26. A Combinatorial Characterization of the Critical Itineraries of a Uniform Dynamical System. https://arxiv.org/abs/1205.5902

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