Entropy Bounds for Endomorphisms Commuting with K Actions
نویسنده
چکیده
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.
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