Critical regularity of invariant foliations (Q1848984)

The paper deals with an open set of symplectic Anosov diffeomorphisms on which there are discrete ``jumps'' in the regularity of the unstable sub-bundle. The author shows that it is either highly irregular almost everywhere \(C^\varepsilon\) only on a negligible set or better than \(C^1\). In the latter case the Hölder exponent of the derivative is either about \(\varepsilon/2\) or almost~1.