In this talk we present a toy model for the (sector) renormalisation of holomorphic maps with an irrationally indifferent fixed points. The model depends on the arithmetic of the rotation number at the fixed point, and exhibits the geometry of a non-degenerate holomorphic map with an irrationally indifferent fixed point. We present some sufficient conditions on a give (sector) renormalisation which guarantees the underlying map has the same dynamics as the one of the toy model.[-]