Petters, AO, *Arnold's singularity theory and gravitational lensing*,
Journal of Mathematical Physics, vol. 34 no. 8
(1993),
pp. 3555-3581 .
**Abstract:**

*Caustics in gravitational lensing are formulated from a symplectic geometric viewpoint. Arnold's singularity theory is then used to give a rigorous local classification of generic gravitational lensing caustics and their evolutions. A local classification is also presented of generic image surfaces, time-delay image surfaces, big caustics, and bicaustics. The results of each classification are discussed and graphically illustrated. © 1993 American Institute of Physics.*