R. de la Llave
Rigidity of
higher dimensional conformal Anosov systems
(86K, TeX)
ABSTRACT. We show that Anosov systems in manifolds with trivial tangent bundles and
with the property that the derivatives of
the return maps at periodic orbits are
multiples of the identity in the stable and unstable bundles
are locally rigid. That is, any other smooth map,
in a $C^1$ neighborhood such that it has the same
Jordan normal form at corresponding periodic orbits is
smoothly conjugate to it.
This generalizes results of \cite{CM}.
We present several arguments for the main results.
In particular, we use
quasi-conformal regularity theory.
We also extend the examples of \cite{L2} to
show that some of the hypothesis we make are indeed
necessary.