  We show that in the Gevrey topology, a $d$-torus flow close enough to linear
with a unique rotation vector $\omega$ is linearizable as long as $\omega$
satisfies a Brjuno type diophantine condition. The proof is based on the fast
convergence under renormalization of the associated Gevrey vector field. It
requires a multidimensional continued fractions expansion of $\omega$, and the
corresponding characterization of the Brjuno type vectors. This demonstrates
that renormalization methods deal very naturally with Gevrey regularity
expressed in the decay of Fourier coefficients. In particular, they provide
linearization for frequencies beyond diophantine in non-analytic topologies.

Dynamical Systems