Isomorphism rigidity in entropy rank two

Manfred Einsiedler; Thomas Ward

doi:10.1007/BF02785368

Isomorphism rigidity in entropy rank two

Manfred Einsiedler, Thomas Ward

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	269-284
Number of pages	16
Journal	Israel Journal of Mathematics
Volume	147
Issue number	1
DOIs	https://doi.org/10.1007/BF02785368
Publication status	Published - 2005

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10.1007/BF02785368

Cite this

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title = "Isomorphism rigidity in entropy rank two",

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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AU - Ward, Thomas

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AB - 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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DO - 10.1007/BF02785368

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VL - 147

SP - 269

EP - 284

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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