# American Institute of Mathematical Sciences

November  2002, 8(4): 931-937. doi: 10.3934/dcds.2002.8.931

## Critical regularity of invariant foliations

 1 Department of Mathematics, Tufts University, Medford, MA 02155-5597

Received  July 2001 Revised  March 2002 Published  July 2002

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 Hölder exponent of the derivative is either about $\epsilon/2$ or almost 1.
Citation: Boris Hasselblatt. Critical regularity of invariant foliations. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 931-937. doi: 10.3934/dcds.2002.8.931
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