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

Hasselblatt, Boris; Pesin, Yakov and Schmeling, Jörg LU (2009) In [unknown]
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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author
organization
publishing date
type
Contribution to journal
publication status
submitted
subject
in
[unknown]
publisher
Historielärarnas förening
ISSN
0439-2434
language
English
LU publication?
yes
id
50f622de-b2e6-41b3-8394-fbd518416092 (old id 945994)
date added to LUP
2009-05-25 16:15:03
date last changed
2016-09-13 15:31:29
@misc{50f622de-b2e6-41b3-8394-fbd518416092,
  abstract     = {We provide a general mechanism for obtaining uniform information from<br/><br>
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.},
  author       = {Hasselblatt, Boris and Pesin, Yakov and Schmeling, Jörg},
  issn         = {0439-2434},
  language     = {eng},
  publisher    = {ARRAY(0x8169c48)},
  series       = {[unknown]},
  title        = {The miracle of Anosov Baire rigidity - nonuniform hyperbolicity everywhere implies uniform hyperbolicity},
  year         = {2009},
}