Prevalence of non-Lipschitz Anosov foliations

Authors:
Boris Hasselblatt and Amie Wilkinson

Journal:
Electron. Res. Announc. Amer. Math. Soc. **3** (1997), 93-98

MSC (1991):
Primary 58F15; Secondary 53C12

DOI:
https://doi.org/10.1090/S1079-6762-97-00030-9

Published electronically:
September 11, 1997

MathSciNet review:
1465582

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Abstract | References | Similar Articles | Additional Information

Abstract: We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems and give open dense sets of codimension one systems where this regularity is not exceeded as well as open dense sets of symplectic, geodesic, and codimension one systems where the analogous regularity results of Pugh, Shub, and Wilkinson are optimal. We produce *open sets* of symplectic Anosov diffeomorphisms and flows with low transverse Hölder regularity of the invariant foliations *almost everywhere*. Prevalence of low regularity of conjugacies on large sets is a corollary. We also establish a new connection between the transverse regularity of foliations and their tangent subbundles.

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Additional Information

**Boris Hasselblatt**

Affiliation:
Department of Mathematics Tufts University Medford, MA 02155-5597

Email:
bhasselb@tufts.edu

**Amie Wilkinson**

Affiliation:
Department of Mathematics Northwestern University Evanston, IL 60208-2730

Email:
wilkinso@math.nwu.edu

DOI:
https://doi.org/10.1090/S1079-6762-97-00030-9

Keywords:
Anosov system,
hyperbolic system,
invariant foliations,
stable foliation,
Anosov splitting,
horospheric foliations,
holonomy,
H\"older structures,
conjugacy

Received by editor(s):
May 9, 1997

Published electronically:
September 11, 1997

Dedicated:
To the memory of Gunnar Hasselblatt, 19.8.1928–12.7.1997

Communicated by:
Krystyna Kuperberg

Article copyright:
© Copyright 1997
American Mathematical Society