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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
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Analysis (Mathematics)
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Geometry
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Mathematical analysis
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Mathematics
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Optics, Lasers, Photonics, Optical Devices
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Physics
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Theoretical, Mathematical and Computational Physics
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Authors:
Arnold, Vladimir Igorevic, 1937-2010
.
Arnold, Vladimir Igorevic 1937-2010
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Corporate Authors:
SpringerLink (Online service)
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Series:
Mathematics and its applications. Soviet series
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Classification:
515
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