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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lipschitz distributions and Anosov flows


Author: Slobodan Simic
Journal: Proc. Amer. Math. Soc. 124 (1996), 1869-1877
MSC (1991): Primary 34C35, 58A30; Secondary 53C12
MathSciNet review: 1328378
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Abstract: We show that if a distribution is locally spanned by Lipschitz vector fields and is involutive a.e., then it is uniquely integrable giving rise to a Lipschitz foliation with leaves of class $ C^{1, \text {Lip}} $. As a consequence, we show that every codimension-one Anosov flow on a compact manifold of dimension $ >3 $ such that the sum of its strong distributions is Lipschitz, admits a global cross section.


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Additional Information

Slobodan Simic
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720
Address at time of publication: Department of Mathematics (M/C 249), University of Illinois of Chicago, 851 S. Morgan Street, Chicago, Illinois 60607-7045
Email: simic@math.uic.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03423-5
PII: S 0002-9939(96)03423-5
Keywords: Distribution, foliation, Anosov flow, cross section
Received by editor(s): December 15, 1994
Additional Notes: Part of this research was supported by the University of California Graduate Fellowship
Communicated by: Linda Keen
Article copyright: © Copyright 1996 American Mathematical Society