New dynamical invariants on hyperbolic manifolds (Q1594900)

Given a closed hyperbolic manifold \(M\) and a flow \(\phi_t\) preserving a measure \(\eta\) on a fiber bundle \(B\) over \(M\), the author constructs a measure \(\rho\), on the unit cotangent bundle over \(M\), which is invariant under the geodesic flow. This is a so-called rotation measure which generalizes a homology rotation vector and exists almost everywhere. It is proved that the system \((\phi_t,\eta)\) is measure theoretically semiconjugate to the geodesic flow on \(M\) with an invariant measure \(\rho\).