We investigate joinings of strongly irreducible totally non-symplectic Anosov ℤk, k ≥ 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 ℤk are conjugate over Q. We also obtain a description of the joining measures modulo the classification of zero entropy measures for the actions.
All Science Journal Classification (ASJC) codes
- Applied Mathematics