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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

MANFRED EINSIEDLER
MANFRED EINSIEDLER
Affiliation:
University of Washington, Department of Mathematics, Box 354350, Seattle WA 98195-4350, USAeinsiedl@math.washington.edu
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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.

Keywords

37A45 (primary)37B5037A3537B40 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 3 , May 2004 , pp. 321 - 331
Copyright
© The London Mathematical Society 2004

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