Entropy bounds for endomorphisms commuting withK actions

G. Morris, T. Ward

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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 Z2-action S on X by continuous automorphisms, then T has infinite entropy.
Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalIsrael Journal of Mathematics
Volume106
Issue number1
DOIs
Publication statusPublished - 1998

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