Evolution of singularities of potential flows in collision-free media and the metamorphosis of caustics in three-dimensional space

DOI10.1007/BF01106069zbMath0583.58019OpenAlexW2075056424MaRDI QIDQ1069196

Vladimir I. Arnold

Publication date: 1986

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01106069

zbMATH Keywords

classification of causticscritical points of surfacesLagrangian mappings

Mathematics Subject Classification ID

Singularities of differentiable mappings in differential topology (57R45) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Wavefronts, caustic sheets, and caustic surfing in gravitational lensing, Mathematics of gravitational lensing: Multiple imaging and magnification, A universal magnification theorem. II. Generic caustics up to codimension five, A universal magnification theorem for higher-order caustic singularities, Arnold’s singularity theory and gravitational lensing

Cites Work

• Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part
• Wave front evolution and equivariant Morse lemma