2012/12/02 by Valentin Afraimovich, Afraimovich, V., M. Courbage +3
Computer Science · Mathematics · Physics and Astronomy · #37E10 #37E45 #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1212.0174
openalex publication_date 2012/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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;