  We develop and illustrate methods to compute all single particle potentials
that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the
switchback potentials can be obtained from the primary potential through
functional transformations. We are thereby able to produce the various branches
of the corresponding analytic potential functions, which have an infinite
number of branch points for generic s>2. We illustrate the methods numerically
for the cases s=5/2 and s=10/3.
