# Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

Artur Avila; Marcelo Viana; Amie Wilkinson

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 6, page 1435-1462
- ISSN: 1435-9855

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topAvila, Artur, Viana, Marcelo, and Wilkinson, Amie. "Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows." Journal of the European Mathematical Society 017.6 (2015): 1435-1462. <http://eudml.org/doc/277612>.

@article{Avila2015,

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.},

author = {Avila, Artur, Viana, Marcelo, Wilkinson, Amie},

journal = {Journal of the European Mathematical Society},

keywords = {Lyapunov exponent; geodesic flow; partial hyperbolicity; disintegration; absolute continuity; rigidity; Lyapunov exponent; geodesic flow; partial hyperbolicity; disintegration; absolute continuity; rigidity},

language = {eng},

number = {6},

pages = {1435-1462},

publisher = {European Mathematical Society Publishing House},

title = {Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows},

url = {http://eudml.org/doc/277612},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Avila, Artur

AU - Viana, Marcelo

AU - Wilkinson, Amie

TI - Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 6

SP - 1435

EP - 1462

AB - 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.

LA - eng

KW - Lyapunov exponent; geodesic flow; partial hyperbolicity; disintegration; absolute continuity; rigidity; Lyapunov exponent; geodesic flow; partial hyperbolicity; disintegration; absolute continuity; rigidity

UR - http://eudml.org/doc/277612

ER -

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