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)|
|Number of pages||43|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - Sep 2018|
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