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

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

TeX source (25K)
DVI (33K)
PostScript (130K)

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