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Abstract:

Questions about the behavior of hyperbolic dynamical systems have typically been tackled through geometric methods, but they can often be reframed as questions on PDEs. We show that the study of the regularity of Anosov foliations leads to a non-linear Ricatti equation, which can be studied through microlocal and paradifferential methods. This is joint work with Colin Guillarmou.

A Non-Linear PDE Approach to Hyperbolic Dynamics