Singularities Of Differentiable Mappings
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Singularities Of Differentiable Mappings
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Author : Harold Levine
language : en
Publisher:
Release Date : 1959
Singularities Of Differentiable Mappings written by Harold Levine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Geometry, Differential categories.
Singularities Of Differentiable Maps Volume 1
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-24
Singularities Of Differentiable Maps Volume 1 written by V.I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.
Singularities Of Differentiable Maps The Classification Of Critical Points Caustics And Wave Fronts Volume Ii Monodromy And Asymptotics Of Integrals
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Author : Vladimir Igorevič Arnolʹd
language : en
Publisher:
Release Date : 1985
Singularities Of Differentiable Maps The Classification Of Critical Points Caustics And Wave Fronts Volume Ii Monodromy And Asymptotics Of Integrals written by Vladimir Igorevič Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Singularities Of Differentiable Maps
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher:
Release Date : 1985
Singularities Of Differentiable Maps written by Vladimir Igorevich Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Differentiable mappings categories.
Singularities Of Differentiable Maps
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularities Of Differentiable Maps written by V.I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Singularities Of Differentiable Maps Volume 2
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Author : Elionora Arnold
language : en
Publisher: Birkhäuser
Release Date : 2012-05-17
Singularities Of Differentiable Maps Volume 2 written by Elionora Arnold and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-17 with Mathematics categories.
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.
Singularities Of Differentiable Maps
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Author : Vladimir I. Arnol'd
language : en
Publisher:
Release Date : 1985
Singularities Of Differentiable Maps written by Vladimir I. Arnol'd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Stable Mappings And Their Singularities
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Author : M. Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stable Mappings And Their Singularities written by M. Golubitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.
Singularities Of Differentiable Maps
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher:
Release Date : 1988
Singularities Of Differentiable Maps written by Vladimir Igorevich Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Differentiable mappings categories.
Singularities Of Differentiable Maps
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Author : Vladimir Igorevič Arnolʹd
language : en
Publisher:
Release Date : 2012
Singularities Of Differentiable Maps written by Vladimir Igorevič Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Differentiable mappings categories.