Singularities of Differentiable Maps, Volume 2 Monodromy and Asymptotics of Integrals /

• Κύριοι συγγραφείς: Arnold, V.I (Συγγραφέας), Gusein-Zade, S.M (Συγγραφέας), Varchenko, A.N (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
• Σειρά: Modern Birkhäuser Classics
• Θέματα: Mathematics.; Algebraic geometry.; Topological groups.; Lie groups.; Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Differential geometry.; Manifolds (Mathematics).; Complex manifolds.; Analysis.; Algebraic Geometry.; Differential Geometry.; Topological Groups, Lie Groups.; Manifolds and Cell Complexes (incl. Diff.Topology).; Applications of Mathematics.

Originally published in the 1980s, Singularities of Differentiable Maps: Monodromy and Asymptotics of Integrals was the second of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory.  This uncorrected softcover reprint of the work b...

Πίνακας περιεχομένων:

• 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.