Entropy bounds for endomorphisms commuting with K actions

Morris, G.; Ward, T.

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
• Public URL: https://durham-repository.worktribe.com/output/1495235