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Measurable rigidity and disjointness for {\mathbb Z}^k actions by toral automorphisms

Published online by Cambridge University Press:  07 May 2002

BORIS KALININ  and
ANATOLE KATOK
BORIS KALININ
Affiliation:
The University of Michigan, Ann Arbor, MI, USA (e-mail: [email protected])
ANATOLE KATOK
Affiliation:
The Pennsylvania State University, University Park, PA, USA (e-mail: [email protected])
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Abstract

We investigate joinings of strongly irreducible totally non-symplectic Anosov {\mathbb Z}^k, k\ge 2 actions by toral automorphisms. We show that the existence of a non-trivial joining has strong implications for these actions, in particular, that the restrictions of the actions to a finite index subgroup of {\mathbb Z}^k are conjugate over {\mathbb Q}. We also obtain a description of the joining measures modulo the classification of zero entropy measures for the actions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 2 , April 2002 , pp. 507 - 523
Copyright
2002 Cambridge University Press

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