Lipschitz distributions and Anosov flows

Author:
Slobodan Simic

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

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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 . As a consequence, we show that every codimension-one Anosov flow on a compact manifold of dimension 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:
https://doi.org/10.1090/S0002-9939-96-03423-5

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