Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail

DOI10.1007/BF01106152zbMath0487.58003OpenAlexW1970171908MaRDI QIDQ1165500

Vladimir I. Arnold

Publication date: 1982

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01106152

zbMATH Keywords

asymptotic raysproblems with constraintsbiasymptotic rayfield of extremals on configuration spaceLagrangian manifold of falling raysLagrangian manifold of the phase space of a variational problemLagrangian manifolds with singularitiesopen swallowtail

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (7)

Singular Lagrangian manifolds and semiclassical analysis. ⋮ Singularities of tangent surfaces to directed curves ⋮ Generating families for images of Lagrangian submanifolds and open swallowtails ⋮ Singularities of Lagrangian varieties and related topics ⋮ Sections of Hamiltonian systems ⋮ Structures symplectiques singulières génériques ⋮ Covariant symplectic geometry of binary forms and singularities of systems of rays

Cites Work

• On singularities of mappings of Euclidean spaces. I. Mappings of the plane into the plane
• Equivalence of glancing hyper-surfaces
• Wave front evolution and equivariant Morse lemma
• Invariants of Finite Reflection Groups
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