  We present a dynamical approach to the study of unordered, attracting
manifolds of retrotone maps commonly known as carrying simplices. Our approach
is novel in that it uses the radial representation of unordered manifolds over
the probability simplex coupled with distances between these manifolds measured
by way of the Harnack and Hausdorff metrics. We establish Kuratowski
convergence of radial representations of unordered manifolds to a unique
function which then provides the locally Lipschitz radial representation of the
carrying simplex.
