CLASSIFYING C1+ STRUCTURES ON DYNAMICAL FRACTALS .2. EMBEDDED TREES

Abstract

We classify the C-1+alpha structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded geometry and with contact points. We used these results in an earlier paper to describe the moduli spaces of smooth conjugacy classes of expanding maps and Markov maps on train tracks. In later papers we will use those results to do the same for pseudo-Anosov diffeomorphisms of surfaces. These results are also used in the classification of renormalisation limits of C-1+alpha diffeomorphisms of the circle.