Upper bounds on the number of images produced by point-mass lenses at different distances

Source abstract

If a light source is sequentially lensed by $n$ intervening point-mass lenses at distinct distances, the number of isolated images for a generic source position cannot be greater than $2\cdot 3^{n-1}$. If lensing shear is present in each lens plane, the image counts could be as large as $4^n$, however. For a general multi-plane point-mass lens system, we also devise the recurrence for the BKK bound on the image counts, which is strictly less than Perry's bound due to the resultant degree for $n\ge 2$. None the less, this bound is still quadratic in the number of lenses on each plane, so is likely to overestimate the true sharp bound, which is expected to grow linearly with the number of lenses.