A Universal Magnification Theorem III. Caustics Beyond Codimension Five

Details A Universal Magnification Theorem III. Caustics Beyond Codimension Five A Universal Magnification Theorem III. Caustics Beyond Codimension Five

2009-09-29

arxiv.org/abs/0909.5235v2

J. Math. Phys. 51, 023503 (2010)

Physics

Mathematical Physics

8 pages

Scientific paper

In the final paper of this series, we extend our results on magnification invariants to the infinite family of A, D, E caustic singularities. We prove that for families of general mappings between planes exhibiting any caustic singularity of the A, D, E family, and for a point in the target space lying anywhere in the region giving rise to the maximum number of lensed images (real pre-images), the total signed magnification of the lensed images will always sum to zero. The proof is algebraic in nature and relies on the Euler trace formula.

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