Uniformly quasiconformal partially hyperbolic systems

Clark Butler, Disheng Xu

Research output: Contribution to journalArticle

1 Scopus citations

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 languageEnglish (US)
Pages (from-to)1085-1127
Number of pages43
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume51
Issue number5
DOIs
StatePublished - Sep 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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