Expansive algebraic actions of discrete residually finite amenable groups and their entropy
| dc.creator | Deninger, Christopher | |
| dc.creator | Schmidt, Klaus | |
| dc.date | 2006-05-29 | |
| dc.date | 2006-10-09 | |
| dc.date.accessioned | 2026-07-07T07:14:36Z | |
| dc.date.available | 2026-07-07T07:14:36Z | |
| dc.description | We 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.description | Using 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.identifier | https://arxiv.org/abs/math/0605723 | |
| dc.identifier | http://arxiv.org/abs/math/0605723 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112940 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Operator Algebras | |
| dc.subject | 37A35; 37A456; 37B05; 37C85 | |
| dc.title | Expansive algebraic actions of discrete residually finite amenable groups and their entropy | |
| dc.type | text |