Petters, AO, *Multiplane gravitational lensing. III. Upper bound on number of images*,
Journal of Mathematical Physics, vol. 38 no. 3
(1997),
pp. 1605-1613 .
**Abstract:**

*The total number of lensed images of a light source undergoing gravitational lensing varies as the source traverses a caustic network. It is rigorously shown that for a pointlike light source not on any caustic, a three-dimensional distribution of g point masses on g lens planes creates at most 2(22(g-1)-1) lensed images of the source (g≥2). This complements previous work [Paper I, J. Math. Phys. 36, 4263 (1995)] that showed at least 2g lensed images occur. Application of the upper bound to the global geometry of caustics is also presented. Our methods are based on a complex formulation of point-mass gravitational lensing and techniques from the theory of resultants. The latter yields a new approach to studying upper bounds on number of lensed images due to point-mass gravitational lens systems. © 1997 American Institute of Physics.*