Singularities of Differentiable Maps, Volume 2

Monodromy and Asymptotics of Integrals

Häftad, Engelska, 2012

AvElionora Arnold,S.M. Gusein-Zade,Alexander N. Varchenko,S. M. Gusein-Zade,S M Gusein-Zade,Alexander N Varchenko

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This reprint covers anatomy and physiology of singularities of differentiable functions. Includes the topological structure of isolated critical points of holomorphic functions, the asymptotic behavior of integrals of the method of stationary phase, and more.

Produktinformation

Utgivningsdatum2012-05-17
Mått155 x 235 x 27 mm
Vikt748 g
FormatHäftad
SpråkEngelska
SerieModern Birkhäuser Classics
Antal sidor492
Upplaga2012
FörlagBirkhauser Boston Inc
ISBN9780817683429

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Part I. The topological structure of isolated critical points of functions.- Introduction.- Elements of the theory of Picard-Lefschetz.- The topology of the non-singular level set and the variation operator of a singularity.- The bifurcation sets and the monodromy group of a singularity.- The intersection matrices of singularities of functions of two variables.- The intersection forms of boundary singularities and the topology of complete intersections.- Part II. Oscillatory integrals.- Discussion of results.- Elementary integrals and the resolution of singularities of the phase.- Asymptotics and Newton polyhedra.- The singular index, examples.- Part III. Integrals of holomorphic forms over vanishing cycles.- The simplest properties of the integrals.- Complex oscillatory integrals.- Integrals and differential equations.- The coefficients of series expansions of integrals, the weighted and Hodge filtrations and the spectrum of a critical point.- The mixed Hodge structure of an isolated critical point of a holomorphic function.- The period map and the intersection form.- References.- Subject Index.