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Isomorphism rigidity in entropy rank two

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Abstract

We study the rigidity properties of a class of algebraic ℤ3-actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine subset. This is applied to show isomorphism rigidity for such actions, and to provide examples of non-isomorphic ℤ3-actions with all their ℤ2-sub-actions isomorphic. The proofs use lexicographic half-space entropies and total ergodicity along critical directions.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box 354350, 98195, Seattle, WA, USA

    Manfred Einsiedler

  2. School of Mathematics, University of East Anglia, NR4 7TJ, Norwich, England

    Thomas Ward

Authors
  1. Manfred Einsiedler
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  2. Thomas Ward
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The second-named author thanks the University of Washington for their hospitality and the support of NSF grant DMS 0222452.

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Einsiedler, M., Ward, T. Isomorphism rigidity in entropy rank two. Isr. J. Math. 147, 269–284 (2005). https://doi.org/10.1007/BF02785368

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  • DOI: https://doi.org/10.1007/BF02785368

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