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${\it\alpha}$-Hölder linearization of hyperbolic diffeomorphisms with resonance

Published online by Cambridge University Press:  11 August 2014

WENMENG ZHANG  and
WEINIAN ZHANG
WENMENG ZHANG
Affiliation:
College of Mathematics Science, Chongqing Normal University, Chongqing 400047, PR China email matzwn@126.com, matzwn@gmail.com
WEINIAN ZHANG
Affiliation:
Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 1 , February 2016 , pp. 310 - 334
Copyright
© Cambridge University Press, 2014 

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