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Entropy bounds for endomorphisms commuting with K actions

Morris, G.; Ward, T.

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Authors

G. Morris

T. Ward



Abstract

Shereshevsky has shown that a shift-commuting homeomorphism from the two-dimensional full shift to itself cannot be expansive, and asked if such a homeomorphism can have finite positive entropy. We formulate an algebraic analogue of this problem, and answer it in a special case by proving the following: if T:X->X is a mixing endomorphism of a compact metrizable abelian group X, and T commutes with a completely positive entropy Z^2-action S on X by continuous automorphisms, then T has infinite entropy.

Citation

Morris, G., & Ward, T. (1998). Entropy bounds for endomorphisms commuting with K actions. Israel Journal of Mathematics, 106(1), 1-12. https://doi.org/10.1007/bf02773458

Journal Article Type Article
Publication Date Jan 1, 1998
Deposit Date Oct 12, 2012
Publicly Available Date Oct 17, 2012
Journal Israel Journal of Mathematics
Print ISSN 0021-2172
Electronic ISSN 1565-8511
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 106
Issue 1
Pages 1-12
DOI https://doi.org/10.1007/bf02773458

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Copyright Statement
The original publication is available at www.springerlink.com





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