Prevalence of nonLipschitz Anosov foliations
Authors:
Boris Hasselblatt and Amie Wilkinson
Journal:
Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 9398
MSC (1991):
Primary 58F15; Secondary 53C12
Published electronically:
September 11, 1997
MathSciNet review:
1465582
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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 021555597
Email:
bhasselb@tufts.edu
Amie Wilkinson
Affiliation:
Department of Mathematics Northwestern University Evanston, IL 602082730
Email:
wilkinso@math.nwu.edu
DOI:
http://dx.doi.org/10.1090/S1079676297000309
PII:
S 10796762(97)000309
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
