A universal magnification theorem for higher-order caustic singularities

DOI10.1063/1.3081055zbMath1202.58021arXiv0811.3447OpenAlexW3100326615MaRDI QIDQ3650468

Arlie O. Petters, Amir Babak Aazami

Publication date: 14 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.3447

zbMATH Keywords

galaxiesgravitational lensesquasarsfour-image regions of swallowtail, elliptic umbilic, and hyperbolic umbilic causticstotal signed magnification

Mathematics Subject Classification ID

Space-time singularities, cosmic censorship, etc. (83C75) Normal forms on manifolds (58K50) Critical points of functions and mappings on manifolds (58K05)

Related Items (5)

Mathematics of gravitational lensing: Multiple imaging and magnification ⋮ A universal magnification theorem. II. Generic caustics up to codimension five ⋮ Geometry of universal magnification invariants ⋮ A universal magnification theorem. III. Caustics beyond codimension 5 ⋮ Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing

Cites Work

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• Evolution of singularities of potential flows in collision-free media and the metamorphosis of caustics in three-dimensional space
• Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities
• Magnification relations in gravitational lensing via multidimensional residue integrals
• Arnold’s singularity theory and gravitational lensing
• A Lefschetz fixed point theorem in gravitational lensing

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