JournalsjemsVol. 17, No. 6pp. 1435–1462

Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

  • Artur Avila

    Université Pierre et Marie Curie, Paris, France

  • Marcelo Viana

    IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

  • Amie Wilkinson

    University of Chicago, USA
Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows cover
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Abstract

We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.

Cite this article

Artur Avila, Marcelo Viana, Amie Wilkinson, Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows. J. Eur. Math. Soc. 17 (2015), no. 6, pp. 1435–1462

DOI 10.4171/JEMS/534