This is the first in a series of papers exploring rigidity properties of hyperbolic actions of Z k or R k for k ≥ 2. We show that for all known irreducible examples, the cohomology of smooth cocycles over these actions is trivial. We also obtain similar Hölder and C1 results via a generalization of the Livshitz theorem for Anosov flows. As a consequence, there are only trivial smooth or Hölder time changes for these actions (up to an automorphism). Furthermore, small perturbations of these actions are Hölder conjugate and preserve a smooth volume.
|Original language||English (US)|
|Number of pages||26|
|Journal||Publications Mathématiques de l'Institut des Hautes Scientifiques|
|State||Published - Dec 1994|
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