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Singularities of Caustics and Wave Fronts
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Catalogue Information
Field name
Details
Dewey Class
515
Title
Singularities
of
Caustics and Wave Fronts ([EBook]) / by V. I. Arnold.
Author
Arnold, Vladimir Igorevic , 1937-2010
Other name(s)
SpringerLink (Online service)
Publication
Dordrecht : Springer Netherlands , 1990.
Physical Details
XIII, 259 pages : online resource.
Series
Mathematics and its applications. Soviet series
0169-6378 ; ; 62
ISBN
9789401133302
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-94-011-3330-2
Links to Related Works
Subject References:
Analysis
.
Analysis (Mathematics)
.
Geometry
.
Mathematical analysis
.
Mathematics
.
Optics, Lasers, Photonics, Optical Devices
.
Physics
.
Theoretical, Mathematical and Computational Physics
.
Authors:
Arnold, Vladimir Igorevic, 1937-2010
.
Arnold, Vladimir Igorevic 1937-2010
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Mathematics and its applications. Soviet series
.
Classification:
515
.
.
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