Critical regularity of invariant foliations

Boris Hasselblatt

doi:10.3934/dcds.2002.8.931

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2002, Volume 8, Issue 4: 931-937. Doi: 10.3934/dcds.2002.8.931

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Critical regularity of invariant foliations

Boris Hasselblatt^1,

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

Received: June 30, 2001

Revised: February 28, 2002

Published: September 2002

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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 Hölder exponent of the derivative is either about $\epsilon/2$ or almost 1.

Keywords:

Critical regularity,
invariant foliations.

Mathematics Subject Classification: 74XX.

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