Isomorphism rigidity in entropy rank two

Details Isomorphism rigidity in entropy rank two Isomorphism rigidity in entropy rank two

2003-09-09

arxiv.org/abs/math/0309161v1

Israel Journal of Mathematics, 147, 269-284, 2005

Mathematics

Dynamical Systems

17 pages

Scientific paper

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.

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