  We study inflection point inflation using Singularity Theory, which relates
degenerate critical points of functions to their local behavior. This approach
illuminates universal features of small-field models and gives analytic control
over parametrized families of scalar potentials near inflationary solutions.
The behavior of the scalar potential is tied to the number of physical input
parameters, which determines a set of universality classes. Within these
classes, we obtain universal scaling relations for density perturbations and
the scale of inflation. In specific models, we show that the scale of
supersymmetry breaking also possesses scaling behavior. We illustrate this
general structure with a specific example: the Racetrack Inflation model in
type IIB string theory, with the inflaton being the real part of the Kahler
modulus, and the input parameters being flux dependent quantities that appear
in the 4D, N=1 superpotential.
