Singularities in variational calculus

DOI10.1007/BF01084817zbMath0554.58010OpenAlexW2053798481MaRDI QIDQ760063

Vladimir I. Arnold

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1007/bf01084817

zbMATH Keywords

symplectic geometrycontact geometrycausticswave frontsobstaclemetamorphosessystems of raysvariational problems with constraints

Mathematics Subject Classification ID

Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items (6)

The local model of an isotropic map-germ arising from one-dimensional symplectic reduction ⋮ Nonholonomic problems and the theory of distributions ⋮ Local diffeomorphisms in symplectic space and Hamiltonian systems with constraints ⋮ Analytic classification of foliations induced by germs of holomorphic vector fields in \((\mathbb {C}^{n},0)\) with non-isolated singularities ⋮ Parametrization of a Singular Lagrangian Variety ⋮ Sections of Hamiltonian systems

Cites Work

• Real two-zone solutions of the sine-Gordon equation
• Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part
• Equivalence of glancing hypersurfaces. II
• On some problems in singularity theory
• Equivalence of glancing hyper-surfaces
• Fourier integral operators. I
• THE GEOMETRY OF BIFURCATION DIAGRAMS
• Wave front evolution and equivariant Morse lemma
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