The miracle of Anosov Baire rigidity - nonuniform hyperbolicity everywhere implies uniform hyperbolicity
Författare
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.
Avdelning/ar
- Matematik LTH
- Dynamical systems
Publiceringsår
2009
Språk
Engelska
Publikation/Tidskrift/Serie
Historielärarnas Förenings Årsskrift
Dokumenttyp
Artikel i tidskrift
Förlag
Historielärarnas förening
Ämne
- Mathematics
Status
Submitted
Forskningsgrupp
- Dynamical systems
ISBN/ISSN/Övrigt
- ISSN: 0439-2434