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Abstract: This thesis is a comprehensive case study of the topological
dynamics, asymptotic geometry, and ergodic theory for the geodesic flow of a class of
3-manifolds which have a non-Riemannian and nonuniformly hyperbolic geometric structure.
These 3-manifolds arise as Hilbert geometries, and they were discovered by Benoist. The
geometric structure forces irregularity of the geodesic flow. ... read more