  We use a renormalisation operator R acting on a space of vector fields on the
d-torus, d>1, to prove the existence of a submanifold of vector fields
equivalent to constant. The result comes from the existence of a fixed point w
of R which is hyperbolic. This is done for a certain class KT of constant
vector fields w, called of 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''.
