α-Hölder linearization of hyperbolic diffeomorphisms with resonance. (11th August 2014) - ZHANG, WENMENG; ZHANG, WEINIAN
Abstract : Concerning hyperbolic diffeomorphisms, one expects a better smoothness of linearization, but it may be confined by resonance among eigenvalues. Hartman gave a three-dimensional analytic mapping with resonance which cannot be linearized by a Lipschitz conjugacy. Since then, efforts have been made to give the α -Hölder continuity of the conjugacy and hope the exponent α<1 can be as large as possible. Recently, it was proved for some weakly resonant hyperbolic diffeomorphisms that α can be as large as we expect. In this paper we prove that this result holds for all C^∞ weakly resonant hyperbolic diffeomorphisms.