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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rotation and entropy


Authors: William Geller and Michal Misiurewicz
Journal: Trans. Amer. Math. Soc. 351 (1999), 2927-2948
MSC (1991): Primary 54H20, 58F99, 58F11
Published electronically: March 29, 1999
MathSciNet review: 1615967
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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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Additional Information

William Geller
Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
Email: wgeller@math.iupui.edu

Michal Misiurewicz
Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
Email: mmisiure@math.iupui.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02344-2
PII: S 0002-9947(99)02344-2
Keywords: Rotation sets, entropy
Received by editor(s): February 22, 1997
Published electronically: March 29, 1999
Additional Notes: The second author was partially supported by NSF grant DMS-9305899.
Article copyright: © Copyright 1999 American Mathematical Society