Genrich Belitskii and Victoria Rayskin
ON THE GROBMAN-HARTMAN THEOREM IN lpha-HOELDER 
CLASS FOR BANACH SPACES
(329K, PDF)

ABSTRACT.  We consider a hyperbolic diffeomorphism in a Banach space with 
a hyperbolic fixed point 0 and a linear part $\Lambda$. We define $\sigma(\Lambda) \in (0,1]$, and prove that for any $lpha < \sigma(\Lambda)$ the diffeomorphism admits local $lpha$-Hoelder linearization.