The miracle of Anosov Baire rigidity - nonuniform hyperbolicity everywhere implies uniform hyperbolicity
Author
Summary, in English
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.
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.
Department/s
- Mathematics (Faculty of Engineering)
- Dynamical systems
Publishing year
2009
Language
English
Publication/Series
Historielärarnas Förenings Årsskrift
Document type
Journal article
Publisher
Historielärarnas förening
Topic
- Mathematics
Status
Submitted
Research group
- Dynamical systems
ISBN/ISSN/Other
- ISSN: 0439-2434