Arithmetic geometric model for the renormalisation of irrationally indifferent attractors

Abstract

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.