Einsiedler, M, Lind, D, Miles, R et al. (1 more author) (2001) Expansive subdynamics for algebraic Zd-actions. Ergodic Theory and Dynamical Systems, 21 (6). 6. pp. 1695-1729. ISSN 0143-3857
Abstract
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 lowerdimensional 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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Sep 2019 15:35 |
Last Modified: | 05 Sep 2019 15:35 |
Published Version: | http://10.0.3.249/S014338570100181X |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/S014338570100181X |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:149685 |