Isomorphism rigidity in entropy rank two

Einsiedler, M.; Ward, T.

Abstract

We study the rigidity properties of a class of algebraic Z^3-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 Z^3-actions with all their Z^2-sub-actions isomorphic. The proofs use lexicographic half-space entropies and total ergodicity along critical directions.

Citation

Einsiedler, M., & Ward, T. (2005). Isomorphism rigidity in entropy rank two. Israel Journal of Mathematics, 147(1), 269-284. https://doi.org/10.1007/bf02785368

• Journal Article Type: Article
• Publication Date: Jan 1, 2005
• Deposit Date: Oct 12, 2012
• Publicly Available Date: Oct 17, 2012
• Journal: Israel Journal of Mathematics
• Print ISSN: 0021-2172
• Electronic ISSN: 1565-8511
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 147
• Issue: 1
• Pages: 269-284
• DOI: https://doi.org/10.1007/bf02785368
• Public URL: https://durham-repository.worktribe.com/output/1502536