Critical itineraries of maps with constant slope and one discontinuity. (English) Zbl 1376.37031
Summary: 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.
MSC:
| 37B10 | Symbolic dynamics |
| 26A18 | Iteration of real functions in one variable |
| 37B15 | Dynamical aspects of cellular automata |
References:
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