The miracle of Anosov Baire rigidity - nonuniform hyperbolicity everywhere implies uniform hyperbolicity

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Abstract

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 contracting invariant cone families, which need not be continuous, then the diffeomor-phism is an Anosov diffeomorphism, i.e., the entire manifold is uniformly hyperbolic.

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Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
JournalHistorielärarnas Förenings Årsskrift
Publication statusSubmitted - 2009
Publication categoryResearch
Peer-reviewedNo