Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows

By Artur Avila, Marcelo Viana, Amie Wilkinson. 2011

83 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c439b23fb04b67638bac8643051d5e7b9ba21f26

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Marcelo Viana
2. Artur Avila
3. David Damanik
4. Jiangong You
5. Qi Zhou
6. R. Krikorian
7. Bassam Fayad
8. Lasse Rempe

In Mathematical Physics

1. Artur Avila
2. Marcelo Viana
3. Jiagang Yang
4. A. Zorich
5. Amie Wilkinson
6. F. R. Hertz
7. David Damanik
8. G. Forni

Citations in the corpus

• Extremal Lyapunov exponents: an invariance principle and applications (2010, methodology): “This can be shown using ideas from Avila, Viana, Wilkinson [7] as we now outline; detailed arguments will appear in [7].”
• Accessibility (2018, unknown): “Additionally, it plays a significant role in analyzing the properties of special ergodic measures, as detailed in [HHTU12, VY13, AVW15, CP23].”