Directional complexity and entropy for lift mappings

Directional complexity and entropy for lift mappings

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 directiona...

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Veröffentlicht in:arXiv.org 2016-09
Hauptverfasser: Afraimovich, V, Courbage, M, Glebsky, L
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Sprache:eng
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Combinatorial analysis
Complexity
Entropy
Markov processes
Windows (intervals)
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creator Afraimovich, V
Courbage, M
Glebsky, L
description 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;
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subjects Combinatorial analysis
Complexity
Entropy
Markov processes
Windows (intervals)
title Directional complexity and entropy for lift mappings
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