Solutions as closed formulas are found for the orbits (x(n), y(n)) of
certain rational, planar maps which permute curves of a conic pencil a
nd consequently reduce to a semi decoupled form b-->B(b), u-->U(b, u).
With the solution formulas it is possible to solve the quantum conduc
tance problem on regular hierarchical lattices in a simple, essentiall
y closed form.