Arnold’s singularity theory and gravitational lensing

DOI10.1063/1.530045zbMath0784.58054OpenAlexW2050242334MaRDI QIDQ3141360

Arlie O. Petters

Publication date: 6 December 1993

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

Full work available at URL: https://doi.org/10.1063/1.530045

zbMATH Keywords

symplectic geometryLagrangian singularitiescausticslight raysgravitational lensingArnold theory

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Applications of dynamical systems (37N99) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General questions in astronomy and astrophysics (85A04)

Related Items

Bounds on number of cusps due to point mass gravitational lenses ⋮ Applications of singularity theory to gravitational lensing. I. Multiple lens planes ⋮ Wavefronts, caustic sheets, and caustic surfing in gravitational lensing ⋮ A symplectic framework for multiplane gravitational lensing ⋮ Symplectic scattering approach to gravitational lensing ⋮ Mathematics of gravitational lensing: Multiple imaging and magnification ⋮ The theory of caustics and wave front singularities with physical applications ⋮ Magnification relations in gravitational lensing via multidimensional residue integrals ⋮ A universal magnification theorem. II. Generic caustics up to codimension five ⋮ Boson stars: Rotation, formation, and evolution ⋮ A universal magnification theorem for higher-order caustic singularities ⋮ A universal magnification theorem. III. Caustics beyond codimension 5 ⋮ Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing

Cites Work

• Reconstructions of fronts and caustics depending on a parameter and versality of mappings
• Evolution of singularities of potential flows in collision-free media and the metamorphosis of caustics in three-dimensional space
• Caustics and non-degenerate Hamiltonians
• Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities
• A gravitational lens produces an odd number of images
• Wave front evolution and equivariant Morse lemma
• Singularities and Plane Maps II: Sketching Catastrophes