Ergodic properties of Gibbs measures on nilpotent covers

Abstract

Let M={\tilde M}/\Gamma be a closed negatively curved manifold with universal covering {\tilde M} and fundamental group \Gamma. Every Gibbs equilibrium state \nu of a Hölder continuous function on the unit tangent bundle T^1M of M projects to a \Gamma-invariant ergodic measure class mc(\nu_+) on the ideal boundary \partial{\tilde M} of {\tilde M}. We show that this measure class is also ergodic under the action of any normal subgroup \Gamma^\prime of \Gamma for which the factor group \Gamma/\Gamma^\prime is nilpotent.