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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: 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

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