Lipschitz distributions and Anosov flows
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- Proc. Amer. Math. Soc. 124 (1996), 1869-1877 Request permission
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.References
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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
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1869-1877
- MSC (1991): Primary 34C35, 58A30; Secondary 53C12
- DOI: https://doi.org/10.1090/S0002-9939-96-03423-5
- MathSciNet review: 1328378