... the values of C outside the Iks.Let us count in each case the number of possibilities:(i) There are at mostNN/n12possibilities, corresponding to the choices of the endpoints of ... details about the partition of unity Ahi.2. Proof of Theorem 1.1.1We show how to prove Theorems 1.1.1 and 1.1.2, using Theorem 1.3.3. Weprove, in fact, the following. Let F ⊂ Σ be an invariant ... that contains the support of Ai in its interior. In fact, the way we smooth the 1IPis to obtain Aiis rather crucial, andwill be discussed in subsection 2.1. Let us only say, for the moment,...