Dual Entropy in Discrete Groups with Amenable Actions

N. P. Brown; E. Germain

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Dual Entropy in Discrete Groups with Amenable Actions

N. P. Brown·E. Germain

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Abstract

We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of entropy agrees with the topological entropy of the induced automorphism on the (compact) dual group of G. We prove a number of basic properties of this dual entropy and give a few calculations. In particular, we are able to give precise calculations for arbitrary automorphisms of crystallographic groups.

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BibTeX RIS

N. P. Brown, E. Germain. 2000-10-12. Dual Entropy in Discrete Groups with Amenable Actions. https://arxiv.org/abs/math/0010122

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