242 citations · 832 across the 17 of their papers we have counts for
18 papers
Magnification Cross Sections for the Elliptic Umbilic Caustic Surface
Amir B. Aazami, Charles R. Keeton, Arlie O. Petters
We show that the asymptotic scaling of the magnification volume cross section corresponding to an elliptic umbilic caustic surface is in the two-image region and $μ^{-2}…
Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing
Amir B. Aazami, Arlie O. Petters, Jeffrey M. Rabin
We provide a geometric explanation for the existence of magnification relations for the A, D, E family of caustic singularities, which were established in recent work. In particula…
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
A. O. Petters, M. C. Werner
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas…
A Universal Magnification Theorem III. Caustics Beyond Codimension Five
Amir B. Aazami, Arlie O. Petters
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…
A Universal Magnification Theorem II. Generic Caustics up to Codimension Five
Amir B. Aazami, Arlie O. Petters
We prove a theorem about magnification relations for all generic general caustic singularities up to codimension five: folds, cusps, swallowtail, elliptic umbilic, hyperbolic umbil…
A Universal Magnification Theorem for Higher-Order Caustic Singularities
Amir B. Aazami, Arlie O. Petters
We prove that, independent of the choice of a lens model, the total signed magnification always sums to zero for a source anywhere in the four-image regions of swallowtail, ellipti…