Classifying C~(1+) structures on dynamical fractals: 2. Embedded trees

摘要

We classify the C~(1+a) structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to j 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 C1+a diffeomorphisms of the circle.