UID:
almahu_9947363381002882
Umfang:
XIII, 259 p.
,
online resource.
ISBN:
9789401133302
Serie:
Mathematics and Its Applications, Soviet Series, 62
Anmerkung:
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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9781402003332
Sprache:
Englisch
DOI:
10.1007/978-94-011-3330-2
URL:
http://dx.doi.org/10.1007/978-94-011-3330-2
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