Invariant fiber measures of angular flows and the Ruelle invariant

Abstract

The Ruelle invariants for non-singular flows of a 3-dimensional manifold and diffeomorphisms of the disc are described by invariant fiber measures, which are families of probability measures on the fibers of the projectivized bundle invariant under the holonomies among almost all fibers. The dynamical properties of invariant fiber measures are also given, which show the benefit of this description.