Directional complexity and entropy for lift mappings
arXiv:1212.0174
Abstract
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: Rotation interval, Space-time window, Directional complexity, Directional entropy;
19p. 3 fig, Discrete and Continuous Dynamical Systems-B (Vol. 20, No. 10) December 2015