Integrals of rapidly oscillating functions and singularities of projections of Lagrangian manifolds

DOI10.1007/BF01077879zbMath0278.57010OpenAlexW2029479859MaRDI QIDQ1842932

Vladimir I. Arnold

Publication date: 1973

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

Full work available at URL: https://doi.org/10.1007/bf01077879

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Singularities of differentiable mappings in differential topology (57R45) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items

Caustics of weakly Lagrangian distributions ⋮ Huygens principle and complex trajectories or Balian and Bloch twenty years after ⋮ An introduction to the semiclassical limit of Euclidean quantum mechanics ⋮ Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems ⋮ Reconstructions of the asymptotics of an integral determined by a hyperbolic unimodal singularity ⋮ Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I ⋮ Applied catastrophe theory in the social and biological sciences ⋮ Efficient formulas for the Maslov canonical operator near a simple caustic ⋮ Generalized Fresnel integrals ⋮ Régularité lipschitzienne et solutions de l'équation des ondes sur une variété riemannienne compacte ⋮ Applications of catastrophe theory to the physical sciences ⋮ Caustics and microfunctions ⋮ Nombre de points entiers dans une famille homothétique de domaines de ${R}$ ⋮ Germes de configurations legendriennes stables et fonctions d'Airy-Weber généralisées. (Germs of stable Legendre configurations and generalized Airy-Weber functions.)

Cites Work

• Structure of representations generated by vectors of highest weight