**This journal is archived by the American Mathematical
Society. The master copy is available at
http://www.ams.org/era/
**

## Prevalence of non-Lipschitz Anosov foliations

### Boris Hasselblatt and Amie Wilkinson

**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.

*Copyright 1997 American Mathematical Society*

**Retrieve entire article **

#### Article Info

- ERA Amer. Math. Soc.
**03** (1997), pp. 93-98
- Publisher Identifier: S 1079-6762(97)00030-9
- 1991
*Mathematics Subject Classification*. Primary 58F15; Secondary 53C12
*Key words and phrases*. Anosov system, hyperbolic system, invariant
foliations, stable foliation, Anosov splitting, horospheric
foliations, holonomy, Hölder structures, conjugacy
- Received by the editors May 9, 1997
- Posted on September 11, 1997
- Communicated by Krystyna Kuperberg
- Comments (When Available)

**Boris Hasselblatt**

Department of Mathematics

Tufts University

Medford, MA 02155-5597

*E-mail address:* `bhasselb@tufts.edu`

**Amie Wilkinson**

Department of Mathematics

Northwestern University

Evanston, IL 60208-2730

*E-mail address:* `wilkinso@math.nwu.edu`

*To the memory of Gunnar Hasselblatt, 19.8.1928-12.7.1997
*

*
*

*
**Electronic Research Announcements of the AMS *Home page