# American Institute of Mathematical Sciences

July  2010, 4(3): 549-569. doi: 10.3934/jmd.2010.4.549

## Zygmund strong foliations in higher dimension

 1 Département de Mathématiques, Université de Cergy-Pontoise, avenue Adolphe Chauvin, 95302, Cergy-Pontoise Cedex, France 2 Institut de Recherche Mathematique Avancée, UMR 7501 du Centre National de la Recherche Scientifique, 7 Rue René Descartes, 67084, Strasbourg Cedex 3 Department of Mathematics, Tufts University, Medford, MA 02155

Received  May 2010 Revised  June 2010 Published  October 2010

For a compact Riemannian manifold $M$, $k\ge2$ and a uniformly quasiconformal transversely symplectic $C^k$ Anosov flow $\varphi$:$\R\times M\to M$ we define the longitudinal KAM-cocycle and use it to prove a rigidity result: $E^u\oplus E^s$ is Zygmund-regular, and higher regularity implies vanishing of the longitudinal KAM-cocycle, which in turn implies that $E^u\oplus E^s$ is Lipschitz-continuous. Results proved elsewhere then imply that the flow is smoothly conjugate to an algebraic one.
Citation: Yong Fang, Patrick Foulon, Boris Hasselblatt. Zygmund strong foliations in higher dimension. Journal of Modern Dynamics, 2010, 4 (3) : 549-569. doi: 10.3934/jmd.2010.4.549
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