Entropy for group endomorphisms and homogeneous spaces
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- by Rufus Bowen
- Trans. Amer. Math. Soc. 153 (1971), 401-414
- DOI: https://doi.org/10.1090/S0002-9947-1971-0274707-X
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Erratum: Trans. Amer. Math. Soc. 181 (1973), 509-510.
Abstract:
Topological entropy ${h_d}(T)$ is defined for a uniformly continuous map on a metric space. General statements are proved about this entropy, and it is calculated for affine maps of Lie groups and certain homogeneous spaces. We compare ${h_d}(T)$ with measure theoretic entropy $h(T)$; in particular $h(T) = {h_d}(T)$ for Haar measure and affine maps $T$ on compact metrizable groups. A particular case of this yields the well-known formula for $h(T)$ when $T$ is a toral automorphism.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 153 (1971), 401-414
- MSC: Primary 28.70; Secondary 22.00
- DOI: https://doi.org/10.1090/S0002-9947-1971-0274707-X
- MathSciNet review: 0274707