Directional complexity and entropy for lift mappings
Valentin Afraimovich Maurice Courbage Lev Glebsky
We introduce and study the notion of a directional complexity and entropy for maps of degree $1$ on the circle. For piecewise affine Markov maps we use symbolic dynamics to relate this complexity to the symbolic complexity. We apply a combinatorial machinery to obtain exact formulas for the directional entropy, to find the maximal directional entropy, and to show that it equals the topological entropy of the map.
keywords: directional entropy. space-time window Rotation interval directional complexity

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