# Expansive subdynamics for algebraic \mathbb{Z}^d-actions

@article{Einsiedler2001ExpansiveSF, title={Expansive subdynamics for algebraic \mathbb\{Z\}^d-actions}, author={Manfred Einsiedler and Douglas Lind and Richard Miles and Thomas Ward}, journal={Ergodic Theory and Dynamical Systems}, year={2001}, volume={21}, pages={1695 - 1729} }

A general framework for investigating topological actions of \mathbb{Z}^d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of \mathbb{R}^d. Here we completely describe this expansive behavior for the class of algebraic \mathbb{Z}^d-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…

## 41 Citations

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