  We study Siegel's center problem on the linearization of germs of
diffeomorphisms in one variable. In addition of the classical problems of
formal and analytic linearization, we give sufficient conditions for the
linearization to belong to some algebras of ultradifferentiable germs closed
under composition and derivation, including Gevrey classes.
  In the analytic case we give a positive answer to a question of J.-C. Yoccoz
on the optimality of the estimates obtained by the classical majorant series
method.
  In the ultradifferentiable case we prove that the Brjuno condition is
sufficient for the linearization to belong to the same class of the germ. If
one allows the linearization to be less regular than the germ one finds new
arithmetical conditions, weaker than the Brjuno condition. We briefly discuss
the optimality of our results.
