On local and global rigidity of quasi-conformal anosov diffeomorphisms

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Abstract

We consider a transitive uniformly quasi-conformal Anosov diffeomorphism [formula omitted] of a compact manifold [formula omitted]. We prove that if the stable and unstable distributions have dimensions greater than two, then [formula omitted] is [formula omitted] conjugate to an affine Anosov automorphism of a finite factor of a torus. If the dimensions are at least two, the same conclusion holds under the additional assumption that [formula omitted] is an infranilmanifold. We also describe necessary and sufficient conditions for smoothness of conjugacy between such a diffeomorphism and a small perturbation. AMS 2000 Mathematics subject classification: Primary 37C; 37D.

Original languageEnglish (US)
Pages (from-to)567-582
Number of pages16
JournalJournal of the Institute of Mathematics of Jussieu
Volume2
Issue number4
DOIs
StatePublished - Oct 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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