Abstract
We study invariant measures with non-vanishing Lyapunov characteristic exponents for commuting diffeomorphisms of compact manifolds. In particular we show that for k = 2, 3 no faithful ℤk real-analytic action on a k-dimensional manifold preserves a hyperbolic measure. In the smooth case similar statements hold for actions faithful on the support of the measure. Generalizations to higher dimension are proved under certain non-degeneracy conditions for the Lyapunov exponents.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 397-411 |
| Number of pages | 15 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 2 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1996 |
All Science Journal Classification (ASJC) codes
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics