The miracle of Anosov Baire rigidity - nonuniform hyperbolicity everywhere implies uniform hyperbolicity
We provide a general mechanism for obtaining uniform information from pointwise data even when the pertinent quantities are highly discontinuous. Some of the applications are almost too good to be believed: If a diffeomorphism of a com-pact Riemannian manifold has nonzero Lyapunov exponents everywhere then the nonwandering set is uniformly hyperbolic. If, in addition, there are expanding and contr
