  We construct the c-function whose gradient determines the RG flow of the
conductivities (sigma_xy and sigma_xx) for a quantum Hall system, subject to
two assumptions. (1) We take the flow to be invariant with respect to the
infinite discrete symmetry group, recently proposed by several workers to
explain the `superuniversality' of the delocalization exponents in these
systems. (2) We also suppose the flow to be `quasi-holomorphic' (which we make
precise) in the sense that it is as close as possible to a one-dimensional flow
in the complex parameter sigma_xy +i sigma_xx. These assumptions together with
the known asymptotic behaviour for large sigma_xx, completely determine the
c-function, and so the phase diagram, for these systems. A complete description
of the RG flow also requires a metric in addition to the c-function, and we
identify the features which are required for this by the RG. A similar
construction produces the c-function for other systems enjoying an infinite
discrete symmetry, such as for supersymmetric QED.
