On a regularity problem occurring in connection with Anosov diffeomorphisms. (English) Zbl 0603.58019

Let \({\mathcal M}\) be a \(C^{\infty}\)-manifold and \({\mathcal F}_ s\) and \({\mathcal F}_ u\) be two Hölder foliations, transverse, and with uniformly \(C^{\infty}\) leaves. If a function f is uniformly \(C^{\infty}\) along the leaves of the two foliations, then it is \(C^{\infty}\) on \({\mathcal M}\). The proof is elementary.


37D99 Dynamical systems with hyperbolic behavior
57R30 Foliations in differential topology; geometric theory
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