Title: Regularity of the horospherical foliation and assumptions on pinching
Abstract: In the study of hyperbolic dynamics, it is an important observation that stable and unstable foliations are not as smooth as the flow, and only holder in general. It is widely believed that they are smooth only when the dynamics is of an algebraic nature. For example the diagonal flow on compact quotients of PSL_2(R). This has lead to investigations on precisely how much holder regularity one can expect. In the classical case of manifolds of variable negative curvature and their geodesic flow, the best results available are expressed in terms of pinching constants. I will recall the main events of that story and then explain why the pinching assumption can be made local instead of global.
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