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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  . 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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- D.V. Anosov: Geodesic flows on closed Riemannian manifolds with negative curvature, Proceedings of the Steklov Math. Inst., no. 90 (1967), AMS Translations (1969) MR 39:3527
- [EG]
- L.C. Evans and R.F. Gariepy: Measure theory and fine properties of functions, Studies in Advanced Math., CRC Press, Boca Raton, 1992 MR 93f:28001
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- J. Franks: Anosov diffeomorphisms, Proc. Symp. in Pure Math., vol. XIV (1970), AMS MR 42:6871
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- E. Ghys: Codimension one Anosov flows and suspensions, Lecture Notes in Math., vol. 1331 (1989), pp.59--72, Springer-Verlag
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- P. Hartman: Ordinary differential equations, Baltimore, 1973 MR 49:9294
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- E. Hille: Lectures on ordinary differential equations, Addison--Wesley, Reading, MA, 1969 MR 40:2939
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- M.W. Hirsch, C.C. Pugh: Stable manifolds and hyperbolic sets, Proc. Symp. in Pure Math., vol. 14 (1970), pp.133--163, AMS, Providence MR 42:6872
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- [Zi]
- W.P. Ziemer: Weakly differentiable functions, GTM 120, Springer--Verlag, New York 1989 MR 91e:46046
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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
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