Abstract
The Hausdorff dimension is obtained for exceptional sets associated with linearising a complex analytic diffeomorphism near a fixed point, and for related exceptional sets associated with obtaining a normal form of an analytic vector field near a singular point. The exceptional sets consist of eigenvalues which do not satisfy a certain Diophantine condition and are 'close' to resonance. They are related to 'lim-sup' sets of a general type arising in the theory of metric Diophantine approximation and for which a lower bound for the Hausdorff dimension has been obtained.
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