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Pointwise hyperbolicity implies uniform hyperbolicity

Hasselblatt, Boris ; Pesin, Yakov and Schmeling, Jörg LU (2014) In Discrete and Continuous Dynamical Systems. Series A 34(7). p.2819-2827
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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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Uniform hyperbolicity, nonuniform hyperbolicity, pointwise hyperbolicity
in
Discrete and Continuous Dynamical Systems. Series A
volume
34
issue
7
pages
2819 - 2827
publisher
American Institute of Mathematical Sciences
external identifiers
  • wos:000328253400008
  • scopus:84892377254
ISSN
1553-5231
DOI
10.3934/dcds.2014.34.2819
language
English
LU publication?
yes
id
52daa59c-6714-4a4f-b955-210c1792da02 (old id 4272235)
date added to LUP
2016-04-01 13:46:09
date last changed
2022-01-27 20:59:28
@article{52daa59c-6714-4a4f-b955-210c1792da02,
  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       = {{Hasselblatt, Boris and Pesin, Yakov and Schmeling, Jörg}},
  issn         = {{1553-5231}},
  keywords     = {{Uniform hyperbolicity; nonuniform hyperbolicity; pointwise hyperbolicity}},
  language     = {{eng}},
  number       = {{7}},
  pages        = {{2819--2827}},
  publisher    = {{American Institute of Mathematical Sciences}},
  series       = {{Discrete and Continuous Dynamical Systems. Series A}},
  title        = {{Pointwise hyperbolicity implies uniform hyperbolicity}},
  url          = {{http://dx.doi.org/10.3934/dcds.2014.34.2819}},
  doi          = {{10.3934/dcds.2014.34.2819}},
  volume       = {{34}},
  year         = {{2014}},
}