Einsiedler, Manfred; Ward, Thomas Fitting ideals for finitely presented algebraic dynamical systems. (English) Zbl 0972.22005 Aequationes Math. 60, No. 1-2, 57-71 (2000). Let \(G\) be a group acting by automorphisms on a compact abelian group \(X\). The Pontryagin dual \(M=\widehat X\), a discrete abelian group, becomes a module of the group ring \(R=\mathbb{Z}[G]\) in a natural way. Algebraic properties of \(M\) then reflect dynamical and topological properties of the action of \(G\) on \(X\). In the paper under consideration the case \(G=\mathbb{Z}^d\) and \(M\) noetherian is studied. The authors show how entropy, expansiveness and periodic point behaviour depend on the structure of the Fitting ideals of a finite free resolution of \(M\). Reviewer: Anton Deitmar (Exeter) Cited in 5 Documents MSC: 22D40 Ergodic theory on groups 37A15 General groups of measure-preserving transformations and dynamical systems Keywords:dynamical systems of algebraic origin; compact abelian group; entropy; Fitting ideals PDFBibTeX XMLCite \textit{M. Einsiedler} and \textit{T. Ward}, Aequationes Math. 60, No. 1--2, 57--71 (2000; Zbl 0972.22005) Full Text: DOI arXiv Link