Local contractions of Banach spaces and spectral gap conditions

摘要

We study the linearization problem for a C-k,C-1, k greater than or equal to 1 contraction of a Banach space E near a fixed point which satisfies a spectral gap condition and a narrow band condition both of order X. We also assume that the part of the spectrum in each band satisfies a finite non-resonant condition of order k relative to itself together with the part that lies in the larger bands. We show that there is a C-k,C- beta linearization for sufficiently small beta > 0. We give a precise estimate on B in terms of the gap and band conditions. (C) 2001 Academic Press. [References: 28]