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INVARIANT SUBSETS AND INVARIANT MEASURES FOR IRREDUCIBLE ACTIONS ON ZERO-DIMENSIONAL GROUPS
Published online by Cambridge University Press: 28 April 2004
Abstract
Algebraic higher-rank actions on connected groups are often remarkably rigid in their topological and measurable structure. In contrast to this, the author of this paper constructs uncountably many closed invariant sets and uncountably many invariant measures with positive entropy for irreducible algebraic ${\mathbb{Z}^d}$-actions on zero-dimensional groups.
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- © The London Mathematical Society 2004
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