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We use a renormalisation operator R acting on a space of vector fields on thed-torus, d>1, to prove the existence of a submanifold of vector fieldsequivalent to constant. The result comes from the existence of a fixed point wof R which is hyperbolic. This is done for a certain class KT of constantvector fields w, called of Koch type. The transformation R is constructed usinga time rescaling, a linear change of basis plus a periodic non-linear mapisotopic to the identity, which we derive by a ``homotopy trick''.Comment: final versio

Renormalization of flows on the multidimensional torus close to aKTfrequency vector