Singularities of Differentiable Maps, Volume 2
Monodromy and Asymptotics of Integrals
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Beschreibung
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 brings its still-relevant content back into the literature, making it available—and affordable—to a global audience of researchers and practitioners.
While the first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable maps—that is, 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. The questions considered here are about the structure of singularities and how they function.
In the first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanishing cycles; distinguished bases; intersection matrices; monodromy groups; the variation operator; and their interconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary phase, which is widely met within applications. The third and last part deals with integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function.
This monograph is suitable for mathematicians, researchers, postgraduates, and specialists in the areas of mechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps.
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. The questions considered are about the structure of singularities and how they function.
Affordable reprint of a classic monograph written by experts in the field Useful for a wide range of applications across disciplines in fields such as differential equations, dynamical systems, optimal control, and optics Suitable for a broad audience of mathematicians, post-graduates, and specialists in the areas of mechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps Includes supplementary material: sn.pub/extras
Autor*in
Elionora Arnold
Themen in »Singularities of Differentiable Maps, Volume 2«
asymptotics intersection forms mixed Hodge structures of singularities monodromy oscillatory integrals singularity theory