Isomorphism rigidity in entropy rank two
Dynamical Systems
2007-05-23 v1
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.
Cite
@article{arxiv.math/0309161,
title = {Isomorphism rigidity in entropy rank two},
author = {Manfred Einsiedler and Thomas Ward},
journal= {arXiv preprint arXiv:math/0309161},
year = {2007}
}
Comments
17 pages