Degeneracies of parametric lens model families near folds and cusps
  We develop an approach to select families of lens models that can describe
doubly and triply gravitationally lensed images near folds and cusps using the
model-independent ratios of lensing-potential derivatives derived in Wagner &
Bartelmann (2015). Models are selected by comparing these model-independent
ratios of potential derivatives to (numerically determined) ratios of potential
derivatives along critical curves for entire lens model families in a given
range of parameter values. This comparison returns parameter ranges which lens
model families can reproduce observation within, as well as sections of the
critical curve where image sets of the observed type can appear. If the
model-independent potential-derivative ratios inferred from the observation
fall outside the range of these ratios derived for the lens model family, the
entire family can be excluded as a feasible model in the given volume in
parameter space. We employ this approach for the family of singular isothermal
spheres with external shear to examples of lensing by a galaxy and two galaxy
clusters (JVAS B1422+231, SDSS J2222+2745, and MACS J1149.5+2223) and show that
the results obtained by our general method are in good agreement with results
of previous model fits.
