Critical regularity of invariant foliations

Abstract

We exhibit an open set of symplectic Anosov diffeomorphisms on which there are discrete jumps in the regularity of the unstable subbundle. It is either highly irregular almost everywhere ($C^\epsilon$ only on a negligible set) or better than $C^1$. In the latter case the Holder exponent of the derivative is either about $\epsilon/2$ or almost 1.