99-137 R. de la Llave
Rigidity of higher dimensional conformal Anosov systems (86K, TeX) Apr 29, 99
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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.

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