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September  2009, 25(3): 981-989. doi: 10.3934/dcds.2009.25.981

Entropy range problems and actions of locally normal groups

Richard Miles 1, and  Michael Björklund 1,

1. 

Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden, Sweden

Received  October 2008 Revised  April 2009 Published  August 2009

This paper deals with the problem of finding the range of entropy values resulting from actions of discrete amenable groups by automorphisms of compact abelian groups. When the acting group $G$ is locally normal, we obtain an entropy formula and show that the full range of entropy values $[0,\infty]$ occurs for actions of $G$. We consider related entropy range problems, give sufficient conditions for zero entropy and, as a consequence, verify the known relationship between completely positive entropy and mixing for these actions.
Keywords: Lehmer's problem., Entropy, algebraic action, locally normal group, entropy range.
Mathematics Subject Classification: 37A35, 37B4.
Citation: Richard Miles, Michael Björklund. Entropy range problems and actions of locally normal groups. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 981-989. doi: 10.3934/dcds.2009.25.981
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