Expansive algebraic actions of discrete residually finite amenable groups and their entropy

Details Expansive algebraic actions of discrete residually finite amenable groups and their entropy Expansive algebraic actions of discrete residually finite amenable groups and their entropy

2006-05-29

arxiv.org/abs/math/0605723v2

Mathematics

Dynamical Systems

Using a recent result of Y. Choi the discussion of expansiveness was strengthened and shortened. The paper will appear in: Erg

Scientific paper

We prove an entropy formula for certain expansive actions of a countable discrete residually finite group $\Gamma $ by automorphisms of compact abelian groups in terms of Fuglede-Kadison determinants. This extends an earlier result proved by the first author under somewhat more restrictive conditions. The main tools for this generalization are a representation of the $\Gamma $-action by means of a `fundamental homoclinic point', and the description of entropy in terms of the renormalized logarithmic growth-rate of the set of $\Gamma_n$-fixed points, where $(\Gamma_n, n\ge1)$ is a decreasing sequence of finite index normal subgroups of $\Gamma $ with trivial intersection.

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