Problem 152

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

Comments

  • rpotrie (2017-02-18 05:14:20 -0800 -0800):

    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.