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Singularities of caustics and wave fronts

Author: V I Arnolʹd
Publisher: Dordrecht, Netherlands ; Boston : Kluwer Academic Publishers, ©1990.
Series: Mathematics and its applications (Kluwer Academic Publishers)., Soviet series ;, 62.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V I Arnolʹd
ISBN: 0792310381 9780792310389
OCLC Number: 22509804
Language Note: Translated from the Russian.
Notes: Translated from the Russian.
Description: xiii, 259 p. : ill. ; 25 cm.
Contents: 1 Symplectic geometry.- 1.1 Symplectic manifolds.- 1.2 Submanifolds of symplectic manifolds.- 1.3 Lagrangian manifolds, fibrations, mappings, and singularities.- 2 Applications of the theory of Lagrangian singularities.- 2.1 Oscillatory integrals.- 2.2 Lattice points.- 2.3 Perestroikas of caustics.- 2.4 Perestroikas of optical caustics.- 2.5 Shock wave singularities and perestroikas of Maxwell sets.- 3 Contact geometry.- 3.1 Wave fronts.- 3.2 Singularities of fronts.- 3.3 Perestroikas of fronts.- 4 Convolution of invariants, and period maps.- 4.1 Vector fields tangent to fronts.- 4.2 Linearised convolution of invariants.- 4.3 Period maps.- 4.4 Intersection forms of period maps.- 4.5 Poisson structures.- 4.6 Principal period maps.- 5 Lagrangian and Legendre topology.- 5.1 Lagrangian and Legendre cobordism.- 5.2 Lagrangian and Legendre characteristic classes.- 5.3 Topology of complex discriminants.- 5.4 Functions with mild singularities.- 5.5 Global properties of singularities.- 5.6 Topology of Lagrangian inclusions.- 6 Projections of surfaces, and singularities of apparent contours.- 6.1 Singularities of projections from a surface to the plane.- 6.2 Singularities of projections of complete intersections.- 6.3 Geometry of bifurcation diagrams.- 7 Obstacle problem.- 7.1 Asymptotic rays in symplectic geometry.- 7.2 Contact geometry of pairs of hypersurfaces.- 7.3 Unfurled swallowtails.- 7.4 Symplectic triads.- 7.5 Contact triads.- 7.6 Hypericosahedral singularity.- 7.7 Normal forms of singularities in the obstacle problem.- 8 Transformation of waves defined by hyperbolic variational principles.- 8.1 Hyperbolic systems and their light hypersurfaces.- 8.2 Singularities of light hypersurfaces of variational systems.- 8.3 Contact normal forms of singularities of quadratic cones.- 8.4 Singularities of ray systems and wave fronts at nonstrict hyperbolic points.
Series Title: Mathematics and its applications (Kluwer Academic Publishers)., Soviet series ;, 62.
Responsibility: by V.I. Arnold.
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'Anyone who is interested in the mathematics of geometric optics, singularities bifurcation theory or just in applications of global analysis may find this as one of the few 'must have' books.' Read more...

 
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