Renormalization of flows on the multidimensional torus close to a KT frequency vector

We use a renormalization operator R acting on a space of vector fields on T-d, d greater than or equal to 2, to prove the existence of a submanifold of vector fields equivalent to constant. The result comes from the existence of a fixed point omega of R which is hyperbolic. This is done for a certain class KTd of frequency vectors omega is an element of R-d, called Koch type. The transformation R is constructed using a time rescaling, a linear change of basis plus a periodic non-linear map isotopic to the identity, which we derive by a 'homotopy trick'.