Abstract
We study smooth volume-preserving perturbations of the time-1 map of the geodesic flow ψt of a closed Riemannian manifold of dimension at least three with constant negative curvature. We show that such a perturbation has equal extremal Lyapunov exponents with respect to volume within both the stable and unstable bundles if and only if it embeds as the time-1 map of a smooth volume-preserving flow that is smoothly orbit equivalent to ψt . Our techniques apply more generally to give an essentially complete classification of smooth, volume-preserving partially hyperbolic diffeomorphisms which satisfy a uniform quasiconformality condition on their stable and unstable bundles and have either compact center foliation with trivial holonomy or are obtained as perturbations of the time-1 map of an Anosov flow.
Original language | English (US) |
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Pages (from-to) | 1085-1127 |
Number of pages | 43 |
Journal | Annales Scientifiques de l'Ecole Normale Superieure |
Volume | 51 |
Issue number | 5 |
DOIs | |
State | Published - Sep 2018 |
All Science Journal Classification (ASJC) codes
- General Mathematics