Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

Artur Avila; Marcelo Viana; Amie Wilkinson

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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http://dx.doi.org/10.4171/JEMS/534

Abstract

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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.

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Avila, 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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