We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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.


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:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher statement:The original publication is available at
Record Created:12 Oct 2012 12:50
Last Modified:17 Oct 2012 10:39

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Look up in GoogleScholar | Find in a UK Library