Expansive subdynamics for algebraic Z^d-actions

EINSIEDLER, Manfred, LIND, Douglas, MILES, Richard and WARD, Thomas (2001). Expansive subdynamics for algebraic Z^d-actions. Ergodic Theory and Dynamical Systems, 21 (6), 1695-1729.

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Link to published version:: https://doi.org/10.1017/S014338570100181X


A general framework for investigating topological actions of Zd on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of Rd. Here we completely describe this expansive behavior for the class of algebraic Zd-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an algebraic variety together with a directional version of Noetherian modules over the ring of Laurent polynomials in several commuting variables. We introduce two notions of rank for topological Zd-actions, and for algebraic Zd-actions describe how they are related to each other and to Krull dimension. For a linear subspace of Rd we define the group of points homoclinic to zero along the subspace, and prove that this group is constant within an expansive component.

Item Type: Article
Departments - Does NOT include content added after October 2018: Faculty of Social Sciences and Humanities > Department of Teacher Education
Identification Number: https://doi.org/10.1017/S014338570100181X
Page Range: 1695-1729
Depositing User: Richard Miles
Date Deposited: 26 Jan 2018 13:09
Last Modified: 18 Mar 2021 16:30
URI: https://shura.shu.ac.uk/id/eprint/17240

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