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

dc.creatorDeninger, Christopher
dc.creatorSchmidt, Klaus
dc.date2006-05-29
dc.date2006-10-09
dc.date.accessioned2026-07-07T07:14:36Z
dc.date.available2026-07-07T07:14:36Z
dc.descriptionWe prove an entropy formula for certain expansive actions of a countable discrete residually finite group $Γ$ 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 $Γ$-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 $Γ_n$-fixed points, where $(Γ_n, n\ge1)$ is a decreasing sequence of finite index normal subgroups of $Γ$ with trivial intersection.
dc.descriptionUsing a recent result of Y. Choi the discussion of expansiveness was strengthened and shortened. The paper will appear in: Ergodic Theory and Dynamical Systems
dc.identifierhttps://arxiv.org/abs/math/0605723
dc.identifierhttp://arxiv.org/abs/math/0605723
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112940
dc.subjectDynamical Systems
dc.subjectOperator Algebras
dc.subject37A35; 37A456; 37B05; 37C85
dc.titleExpansive algebraic actions of discrete residually finite amenable groups and their entropy
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