00-237 Mohamed S. ElBialy
Local Contractions of Banach Spaces and Spectral Gap Conditions (111K, LaTeX 2e) May 19, 00
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Abstract. In this work we study the linearization problem for a \$C^{k,1}, k\geq 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 \$k\$. We also assume that the part of the spectrum in each band satisfies a finite nonresonant 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,\gb}\$ linearization for sufficiently small \$\gb > 0\$. We give a precise estimate on \$\gb\$ in terms of the gap and band conditions.

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