  In this paper we build a geometric model for the renormalisation of
irrationally indifferent fixed points. The geometric model incorporates the
fine arithmetic properties of the rotation number at the fixed point. Using
this model for the renormalisation, we build a topological model for the
dynamics of a holomorphic map near an irrationally indifferent fixed point.
Then, we explain the topology of the maximal invariant set for the model, and
also explain the dynamics of the map on the maximal invariant set.
