Abstract
We classify the C1+a 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 C1+a diffeomorphisms of the circle.

Abstract
We consider a symmetric Stackelberg model in which there is asymmetric demand information owned by first and second movers. We analyse the advantages of leadership and flexibility, and prove that when the leading firm faces demand uncertainty, but the follower does not, the first mover does not necessarily have advantage over the second mover. Moreover, we show that the advantage of one firm over the other depends upon the demand fluctuation and also upon the degree of substitutability of the products.

Abstract
We consider two Cournot firms, one located in the home country and the other in the foreign country, producing substitute goods for consumption in a third country. We suppose that neither the home government nor the foreign firm know the costs of the home firm, while the foreign firm cost is common knowledge. We determine the separating sequential equilibrium outputs.

Abstract
We introduce the notion of golden tilings, and we prove a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, (ii) affine classes of golden tilings and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences.

Abstract
Hyperbolic invariant sets A of C1+gamma diffeomorphisms where either the stable or unstable leaves are 1-dimensional are considered in this paper, Under the assumption that the A has local product structure, the authors prove that the holonomies between the 1-dimensional leaves are C1+alpha for some 0 < alpha < 1.

Abstract
We construct a Teichmuller space for the C1+-conjugacy classes of hyperbolic dynamical systems on surfaces. After introducing the notion of an HR structure which associates an affine structure with each of the stable and unstable laminations, we show that there is a one-to-one correspondence between these HR structures and the C1+-conjugacy classes. As part of the proof we construct a canonical representative dynamical system for each HR structure. This has the smoothest holonomies of any representative of the corresponding C1+-conjugacy class. Finally, we introduce solenoid functions and show that they provide a good Teichmuller space.