Abstract
We show C∞ local rigidity for Z{double-struck}k (k ≥ 2) higher rank partially hyperbolic actions by toral automorphisms, using a generalization of the KAM (Kolmogorov-Arnold-Moser) iterative scheme. We also prove the existence of irreducible genuinely partially hyperbolic higher rank actions on any torus T{double-struck}N for any even N ≥ 6.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1805-1858 |
| Number of pages | 54 |
| Journal | Annals of Mathematics |
| Volume | 172 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2010 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty