Abstract
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) |
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Pages (from-to) | 131-156 |
Number of pages | 26 |
Journal | Publications Mathématiques de l'Institut des Hautes Scientifiques |
Volume | 79 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1994 |
All Science Journal Classification (ASJC) codes
- General Mathematics