On the size of the domain of linearization in Hartman's theorem (Q1102010)

An estimate is given for the size of a neighbourhood U of a hyperbolic fixed point (zero) of a \(C^ 1\) diffeomorphism f (resp. vector field X) on a Banach space such that f (resp. X) is conjugate to its differential on U. The existence of such a neighbourhood U follows from the well-known Grobman-Hartman theorem, cf. for example \textit{Z. Nitecki} [Differentiable dynamics. An introduction to the orbit structure of diffeomorphisms (1971; Zbl 0246.58012)].