  We study the fixed points of the q-bracket on the complex unit disk, and
prove the following. The set of (nontrivial) pairs (x,q) such that [x]_q=x form
a manifold whose standard projections both have degree p-2. There is an
analytic function Q(X) taking x to q for which [x]_q=x, which is a (bijective)
contraction unless the multiplicity of the residue of x in the fiber over q is
two. The restriction of the theory to Z_p is trivial unless p=3.
