The Theory of Caustics and Wavefront Singularities with Physical Applications

Abstract

This is intended as an introduction to and review of the work of V, Arnold and his collaborators on the theory of Lagrangian and Legendrian submanifolds and their associated maps. The theory is illustrated by applications to Hamilton-Jacobi theory and the eikonal equation, with an emphasis on null surfaces and wavefronts and their associated caustics and singularities.

Figs. not included

References in corpus (2)

• An Exact Universal Gravitational Lensing Equation
• The Eikonal Equation in Flat Space: Null Surfaces and Their Singularities I

Cited by in corpus (24)

• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Caustics for Spherical Waves
• Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
• Cosmological perturbations for two cold fluids in $\Lambda$CDM
• Strong lensing, plane gravitational waves and transient flashes
• Fermat Potentials for Non-Perturbative Gravitational Lensing
• Horizons in a binary black hole merger I: Geometry and area increase
• Measuring emission coordinates in a pulsar-based relativistic positioning system
• Tracking Black Holes in Numerical Relativity
• The lightcone of Gödel-like spacetimes
• Solving two-point boundary value problems using generating functions: Theory and Applications to optimal control and the study of Hamiltonian dynamical systems
• Wavefronts and Light Cones for Kerr Spacetimes
• Strong-field gravitational lensing by black holes
• Gravitational Lensing from a Spacetime Perspective
• Solutions and Singularities of the Semigeostrophic Equations via the Geometry of Lagrangian Submanifolds
• Revisiting the Light Cone of the Goedel Universe
• The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method
• The Hawking Energy on the Past Lightcone in Cosmology
• Null Geodesics and Wave Front Singularities in the Godel Space-time
• Examining the Kerr Metric through Wave Fronts of Null Geodesics
• Covariant Evolution of Gravitoelectromagnetism
• $S_t^1\times S_s^1$-valued lightcone Gauss map of a Lorentzian surface in semi-Euclidean 4-space
• Linking, Legendrian linking and causality
• Spacetime Perspective of Gravitational Lensing in Perturbed Cosmologies