Lipschitz distributions and Anosov flows

Simic, Slobodan

doi:10.1090/S0002-9939-96-03423-5

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.

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