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

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 $β$-expansions (with positive or negative $β$) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

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