Rotation and entropy

Geller, William; Misiurewicz, Michał

doi:10.1090/S0002-9947-99-02344-2

Rotation and entropy
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by William Geller and Michał Misiurewicz

Trans. Amer. Math. Soc. 351 (1999), 2927-2948

DOI: https://doi.org/10.1090/S0002-9947-99-02344-2

Published electronically: March 29, 1999

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Abstract:

For a given map $f: X \to X$ and an observable $\varphi : X \to \mathbb {R} ^{d},$ rotation vectors are the limits of ergodic averages of $\varphi .$ We study which part of the topological entropy of $f$ is associated to a given rotation vector and which part is associated with many rotation vectors. According to this distinction, we introduce directional and lost entropies. We discuss their properties in the general case and analyze them more closely for subshifts of finite type and circle maps.

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