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Entropy bounds for endomorphisms commuting with K actions.

Morris, G. and Ward, T. (1998) 'Entropy bounds for endomorphisms commuting with K actions.', Israel journal of mathematics., 106 (1). pp. 1-12.

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.

Item Type:Article
Full text:PDF - Accepted Version (216Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/BF02773458
Publisher statement:The original publication is available at www.springerlink.com
Record Created:12 Oct 2012 12:50
Last Modified:17 Oct 2012 10:39

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