Singularities of Differentiable Maps, Volume 2

Monodromy and Asymptotics of Integrals

AvElionora Arnold,S.M. Gusein-Zade

Häftad, Engelska, 2012

Del i serien Modern Birkhäuser Classics

956 kr

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Beskrivning

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

Utgivningsdatum:2012-05-17
Mått:155 x 235 x 27 mm
Vikt:748 g
Format:Häftad
Språk:Engelska
Serie:Modern Birkhäuser Classics
Antal sidor:492
Upplaga:2012
Förlag:Birkhauser Boston Inc
ISBN:9780817683429

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Innehållsförteckning

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.

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