Entropy bounds for endomorphisms commuting withK actions

Morris, G. and Ward, T. (1998) Entropy bounds for endomorphisms commuting withK actions. Israel Journal of Mathematics, 106 (1). pp. 1-12. ISSN 0021-2172

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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 Z2-action S on X by continuous automorphisms, then T has infinite entropy.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 15 Dec 2022 02:01
URI: https://ueaeprints.uea.ac.uk/id/eprint/18605
DOI: 10.1007/BF02773458

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