Critical regularity of invariant foliations

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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

Abstract
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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.

Keywords: invariant foliations., Critical regularity.

Mathematics Subject Classification: 74X.

Citation: Boris Hasselblatt. Critical regularity of invariant foliations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 931-937. doi: 10.3934/dcds.2002.8.931

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