Geodesic
Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows
Journal of the European Mathematical Society, Tome 17 (2015) no. 6, pp. 1435-1462 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/534
Classification : 37-XX
Keywords: Lyapunov exponent, geodesic flow, partial hyperbolicity, disintegration, absolute continuity, rigidity 
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     author = {Artur Avila and Marcelo Viana and Amie Wilkinson},
     title = {Absolute continuity, {Lyapunov} exponents and rigidity {I:} geodesic flows},
     journal = {Journal of the European Mathematical Society},
     pages = {1435--1462},
     year = {2015},
     volume = {17},
     number = {6},
     doi = {10.4171/jems/534},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/534/}
}
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Artur Avila; Marcelo Viana; Amie Wilkinson. Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows. Journal of the European Mathematical Society, Tome 17 (2015) no. 6, pp. 1435-1462. doi: 10.4171/jems/534

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