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Published online by Cambridge University Press: 29 May 2025
In this article we describe some dynamical properties of one-parameter unipotent flows on the frame bundle of a convex cocompact hyperbolic 3-manifold.
Much effort and study have been spent in the case of manifolds with finite volume, and quite a rich theory has developed in this case. The case of infinite volume manifolds, however, is far less understood. The goal here is to highlight some of the difficulties one faces, and possible modifications, in extending techniques developed in the finite volume case to the case of infinite volume manifolds.
Throughout, G = PSL2 (ℂ), the group of orientation-preserving isometries of the hyperbolic space ℍ3. We letbe a nonelementary discrete subgroup of G which is convex cocompact, that is, the convex hull of the limit set of⌈ is compact modulo . Equivalently, ⌈\ ℍ3 admits a finite sided fundamental domain with no cusps.
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