Problem 152

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$T:M \to M \;  C^\infty $ Anosov. $f \in C^r $ and $f(x) = u(x) - u(Tx) .$   Does  $u \in C^r?$ ($r\geq 2$).




See de la Llave, R.Marco, J. M.Moriyón, R. Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation. Ann. of Math. (2) 123 (1986), no. 3, 537--611. See also: Journé, J.-L., A regularity lemma for functions of several variables, Rev. Mat.Iberoamericana 4 (1988), no. 2, 187–193. 

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