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Books > Science & Mathematics > Mathematics > Geometry > Analytic geometry
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Singularities of Differentiable Maps - Volume II Monodromy and Asymptotic Integrals (Paperback, Softcover reprint of the original 1st ed. 1988)
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Singularities of Differentiable Maps - Volume II Monodromy and Asymptotic Integrals (Paperback, Softcover reprint of the original 1st ed. 1988)
Series: Monographs in Mathematics, 83
Expected to ship within 10 - 15 working days
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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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