Nonuniform hyperbolicity in Hilbert geometries

Bray, Sarah.


  • 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. In p... read more
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