Pointwise hyperbolicity implies  uniform hyperbolicity

Boris Hasselblatt; Yakov Pesin; Jörg Schmeling

doi:10.3934/dcds.2014.34.2819

Article Contents

2014, Volume 34, Issue 7: 2819-2827. Doi: 10.3934/dcds.2014.34.2819

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Pointwise hyperbolicity implies uniform hyperbolicity

1.
Department of Mathematics, Tufts University, Medford, MA 02155
2.
Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802
3.
Department of Mathematics, Lund Institute of Technology, Lunds Universitet, Box 118, SE-22100 Lund

Received: February 28, 2013

Revised: September 30, 2013

Published: June 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 37D20, 37D25; Secondary: 54H05.

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References

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