Isomorphism rigidity in entropy rank two

2003/09/09 by Manfred Einsiedler, Thomas Ward
Mathematics · #math.DS #msc:22D40 #msc:37A15 #msc:52B11

paper · pdf

published as Israel Journal of Mathematics, 147, 269-284, 2005 · 17 pages

arxiv created 2003/09/09 · arxiv updated 2009/12/01

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.

Related

• Isomorphism rigidity of algebraic Z^d-actions
• Isomorphism rigidity of commuting automorphisms
• Rigidity of the measurable structure for algebraic actions of higher rank abelian groups
• Rigidity properties for commuting automorphisms on tori and solenoids
• Rigidity of non-maximal torus actions, unipotent quantitative recurrence, and Diophantine approximations