HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Dual entropy in discrete groups with amenable actions

Abstract : Let G be a discrete group which admits an amenable action on a compact space and \gamma \in \textrm{Aut}(G) be an automorphism. We define a notion of entropy for \gamma and denote the invariant by ha(\gamma). This notion is dual to classical topological entropy in the sense that if G is abelian then ha(\gamma) = h_{\rm Top}(\hat{\gamma}) where h_{\rm Top}(\hat{\gamma}) denotes the topological entropy of the induced automorphism \hat{\gamma} of the (compact, abelian) dual group \hat{G}. ha(\cdot) enjoys a number of basic properties which are useful for calculations. For example, it decreases in invariant subgroups and certain quotients. These basic properties are used to compute the dual entropy of an arbitrary automorphism of a crystallographic group.
Document type :
Journal articles
Complete list of metadata

https://hal-normandie-univ.archives-ouvertes.fr/hal-01876553
Contributor : Emmanuel Germain Connect in order to contact the contributor
Submitted on : Tuesday, September 18, 2018 - 3:14:45 PM
Last modification on : Tuesday, October 19, 2021 - 11:33:54 PM

Links full text

Identifiers

Collections

Citation

Emmanuel Germain, Nathanial Brown. Dual entropy in discrete groups with amenable actions. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2002, 22 (03), ⟨10.1017/S0143385702000366⟩. ⟨hal-01876553⟩

Share

Metrics

Record views

29