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Singularities of Differentiable Maps: Volume II Monodromy and Asymptotic Integrals (Monographs in Mathematics) (Vol 2) ePub download

by V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade

  • Author: V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade
  • ISBN: 0817631852
  • ISBN13: 978-0817631857
  • ePub: 1688 kb | FB2: 1625 kb
  • Language: English
  • Category: Mathematics
  • Publisher: Birkhäuser; 1988 edition (October 1, 1988)
  • Pages: 492
  • Rating: 4.7/5
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Singularities of Differentiable Maps: Volume II Monodromy and Asymptotic Integrals (Monographs in Mathematics) (Vol 2) ePub download

volume is the second volume of the book "Singularities of Differentiable Maps" by . Arnold, A. N. Varchenko and S. M. Gusein-Zade.

volume is the second volume of the book "Singularities of Differentiable Maps" by . The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982.

Singularities of Differentiable Maps. Monographs in Mathematics. See any care plans, options and policies that may be associated with this product. Electrode, App-product, Comp-283036184, DC-prod-dfw8, ENV-prod-a, PROF-PROD, VER-29.

Singularities of differentiable maps by Arnolʹd, V. . Monodromy and asymptotic integrals (Monographs in Mathematics). by Arnolʹd, V. Published October 1, 1988 by Birkhauser.

I. Arnold, S. Gusein-Zade, and A. Varchenko. Part II. Oscillatory integrals. Discussion of results. The coefficients of series expansions of integrals, the weighted and Hodge filtrations and the spectrum of a critical point

I. Publisher: Birkhäuser. 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. 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.

Singularities of Differentiable Maps (Monographs in Mathematics). Singularities of differentiable maps. Singularities of Differentiable Maps, Volume 1: Classification of Critical Points, Caustics and Wave Fronts. Topology of Singular Fibers of Differentiable Maps. The classification of critical points caustics and wave fronts. Asymptotics of integrals (2007)(en)(9s).

¿¿The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originally published as Volume 82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions.

from the Russian by Hugh Porteous and revised by the authors and James Montaldi.

Varchenko introduced the asymptotic mixed Hodge structure on the cohomology, vanishing at a critical point of a function, by.Arnolʹd, V. Guseĭn-Zade, S. Varchenko, A.

Varchenko introduced the asymptotic mixed Hodge structure on the cohomology, vanishing at a critical point of a function, by studying asymptotics of integrals of holomorphic differential forms over families of vanishing cycles. Such an integral depends on the parameter – the value of the function. The integral has two properties: how fast it tends to zero, when the parameter tends to the critical value, and how the integral changes, when the parameter goes around the critical value. Vol. I. The classification of critical points, caustics and wave fronts.

Volume II Monodromy and Asymptotic Integrals. volume is the second volume of the book "Singularities of Differentiable Maps" by . The first volume, subtitled "Classification of critical points, caustics and wave fronts", wa. 985 Book. Volume I: The Classification of Critical Points Caustics and Wave Fronts. there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science.

The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982. It will be referred to in this text simply as "Volume 1". Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation.
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