${\it\alpha}$-Hölder linearization of hyperbolic diffeomorphisms with resonance. (11th August 2014)

• Record Type: Journal Article
• Authors: ZHANG, WENMENG; ZHANG, WEINIAN
• Is Part Of: Ergodic theory and dynamical systems. Volume 36:Number 1(2016:Feb.)
• Page Start: 310
• Page End: 334
• Publication Date: 2014-08-11
• Subjects: Ergodic theory -- Periodicals; Differentiable dynamical systems -- Periodicals; 515.42
• DOI: 10.1017/etds.2014.51
• Languages: English
• ISSNs: 0143-3857

Abstract

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 ${\it\alpha}$ -Hölder continuity of the conjugacy and hope the exponent ${\it\alpha}<1$ can be as large as possible. Recently, it was proved for some weakly resonant hyperbolic diffeomorphisms that ${\it\alpha}$ can be as large as we expect. In this paper we prove that this result holds for all $C^{\infty }$ weakly resonant hyperbolic diffeomorphisms.