Pointwise hyperbolicity implies uniform hyperbolicity

Boris Hasselblatt; Yakov Pesin; Jörg Schmeling

doi:10.3934/dcds.2014.34.2819

Pointwise hyperbolicity implies uniform hyperbolicity

Boris Hasselblatt, Yakov Pesin, Jörg Schmeling

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2819-2827
Number of pages	9
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	34
Issue number	7
DOIs	https://doi.org/10.3934/dcds.2014.34.2819
State	Published - Jul 2014

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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title = "Pointwise hyperbolicity implies uniform hyperbolicity",

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.",

author = "Boris Hasselblatt and Yakov Pesin and J{\"o}rg Schmeling",

year = "2014",

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doi = "10.3934/dcds.2014.34.2819",

language = "English (US)",

volume = "34",

pages = "2819--2827",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

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AU - Pesin, Yakov

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AB - 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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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

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Pointwise hyperbolicity implies uniform hyperbolicity

Abstract

All Science Journal Classification (ASJC) codes

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