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Pointwise hyperbolicity implies uniform hyperbolicity

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  • We provide a general mechanism for obtaining uniform information from pointwise data. For instance, a diffeomorphism of a compact Riemannian manifold with pointwise expanding and contracting continuous invariant cone families is an Anosov diffeomorphism, i.e., the entire manifold is uniformly hyperbolic.
    Mathematics Subject Classification: Primary: 37D20, 37D25; Secondary: 54H05.


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