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Titlebook: Singularities of Differentiable Maps; Volume II Monodromy V. I. Arnold,S. M. Gusein-Zade,A. N. Varchenko Book 1988 Springer Science+Busine

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发表于 2025-3-21 18:25:22 | 显示全部楼层 |阅读模式
书目名称Singularities of Differentiable Maps
副标题Volume II Monodromy
编辑V. I. Arnold,S. M. Gusein-Zade,A. N. Varchenko
视频video
丛书名称Monographs in Mathematics
图书封面Titlebook: Singularities of Differentiable Maps; Volume II Monodromy  V. I. Arnold,S. M. Gusein-Zade,A. N. Varchenko Book 1988 Springer Science+Busine
描述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 p
出版日期Book 1988
关键词Calculation; Lie; Volume; algebra; behavior; bifurcation; character; classification; differential equation; h
版次1
doihttps://doi.org/10.1007/978-1-4612-3940-6
isbn_softcover978-1-4612-8408-6
isbn_ebook978-1-4612-3940-6Series ISSN 1017-0480 Series E-ISSN 2296-4886
issn_series 1017-0480
copyrightSpringer Science+Business Media New York 1988
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发表于 2025-3-21 20:45:15 | 显示全部楼层
The singular index, examplesinct singular indices. Third, the existence of a critical point in which the singular index is not equal to the remoteness. Finally, the existence of a critical point in which the principal part of the Taylor series is ℝ-nondegenerate but the remoteness of the Newton polyhedron is greater than the oscillation index.
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The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectruuss-Manin connection) sections of the homological Milnor fibration. Therefore (if the form is fixed) each coefficient of the series is a linear function on the space of covariantly constant sections of the homological Milnor fibration, that is it is a covariantly constant section of the cohomological Milnor fibration.
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Introductionsets. The topology of the level sets or infra-level sets of smooth real-valued functions on manifolds may be investigated with the help of Morse theory (see [255]). The idea there is to study the change of structure of infra-level sets and level sets of functions upon passing critical values. In the
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The bifurcation sets and the monodromy group of a singularityromy group…) are closely linked to such objects as the level and function bifurcation sets of the singularity, its resolution and its polar curve. Several of these links will be discussed in this chapter.
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Elementary integrals and the resolution of singularities of the phasethe asymptotics of an oscillatory integral and the poles of the meromorphic function ., Where ƒ is the phase, and ϕ is the amplitude of the oscillatory integral. We shall introduce the discrete characteristics of the resolution of the singularity of a critical point of the phase: the weight of the r
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