The miracle of Anosov Baire rigidity - nonuniform hyperbolicity everywhere implies uniform hyperbolicity
(2009) In Historielärarnas Förenings Årsskrift- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/945994
- author
- Hasselblatt, Boris ; Pesin, Yakov and Schmeling, Jörg LU
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- submitted
- subject
- in
- Historielärarnas Förenings Årsskrift
- publisher
- Historielärarnas förening
- ISSN
- 0439-2434
- language
- English
- LU publication?
- yes
- id
- 50f622de-b2e6-41b3-8394-fbd518416092 (old id 945994)
- date added to LUP
- 2016-04-04 13:36:38
- date last changed
- 2019-11-25 09:02:58
@article{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 = {{Historielärarnas förening}}, series = {{Historielärarnas Förenings Årsskrift}}, title = {{The miracle of Anosov Baire rigidity - nonuniform hyperbolicity everywhere implies uniform hyperbolicity}}, year = {{2009}}, }