# 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}
}
• Published 27 April 2001
• Mathematics
• Ergodic Theory and Dynamical Systems
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…
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