Currently displaying 1 – 7 of 7

Showing per page

Order by Relevance | Title | Year of publication

Nonuniform center bunching and the genericity of ergodicity among C 1 partially hyperbolic symplectomorphisms

Artur AvilaJairo BochiAmie Wilkinson — 2009

Annales scientifiques de l'École Normale Supérieure

We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns–Wilkinson and Avila–Santamaria–Viana. Combining this new technique with other constructions we prove that C 1 -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.

Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

Artur AvilaMarcelo VianaAmie Wilkinson — 2015

Journal of the European Mathematical Society

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.

Page 1

Download Results (CSV)