Journé, Jean-Lin On a regularity problem occurring in connection with Anosov diffeomorphisms. (English) Zbl 0603.58019 Commun. Math. Phys. 106, 345-351 (1986). 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. Cited in 16 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior 57R30 Foliations in differential topology; geometric theory Keywords:Hölder foliations; \(C^{\infty }\) leaves × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Campanato, S.: Proprietá dí una famiglia dí spazi funzionali. Ann. Sc. Norm. Super. Pisa18, 137-160 (1964) · Zbl 0133.06801 [2] de la Llave, R.: Invariants for smooth conjugacy of hyperbolic systems. II (submitted to Commun. Math. Phys.) · Zbl 0673.58036 [3] de la Llave, R., Marco, J.M., Moriyon, R.: Canonical perturbation theories for Anosov’s systems and regularity results for the Livsic’s Cohomology Equation. Ann. Math. to appear. See also Bull. Am. Math. Soc.12, 1, 91-94 (1985) · Zbl 0576.58011 · doi:10.1090/S0273-0979-1985-15298-X [4] Marco, J.M., Moriyon, R.: Invariants for smooth conjugacy of hyperbolic systems. I (submitted to Commun. Math. Phys.) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.