Singularities Of Differentiable Maps Volume 1

Author : V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251545

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Singularities of Differentiable Maps by V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade Pdf

... 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. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).

Author : V.I. Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 52,6 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780817683405

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Singularities of Differentiable Maps, Volume 1 by V.I. Arnold,S.M. Gusein-Zade,Alexander N. Varchenko Pdf

​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.

Author : Vladimir Igorevič Arnolʹd,Sabir Goussein-Zadé,Aleksandr Nikolaevich Varchenko
Publisher : Unknown
Page : 874 pages
File Size : 40,8 Mb
Release : 1985
Category : Electronic
ISBN : 3764331879

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Singularities of Differentiable Maps: The classification of critical points, caustics and wave fronts ; Volume II, Monodromy and asymptotics of integrals by Vladimir Igorevič Arnolʹd,Sabir Goussein-Zadé,Aleksandr Nikolaevich Varchenko Pdf

Author : V.I. Arnold,Alexander Varchenko,S.M. Gusein-Zade
Publisher : Birkhäuser
Page : 396 pages
File Size : 45,6 Mb
Release : 2011-12-06
Category : Mathematics
ISBN : 1461251559

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Singularities of Differentiable Maps by V.I. Arnold,Alexander Varchenko,S.M. Gusein-Zade Pdf

... 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. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).

Author : V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239406

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Singularities of Differentiable Maps by V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade Pdf

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.

Author : Vladimir I. Arnol'd
Publisher : Unknown
Page : 382 pages
File Size : 54,5 Mb
Release : 1985
Category : Electronic
ISBN : 3764331879

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Singularities of Differentiable Maps by Vladimir I. Arnol'd Pdf

Author : Elionora Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 44,9 Mb
Release : 2012-05-16
Category : Mathematics
ISBN : 9780817683436

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Singularities of Differentiable Maps, Volume 2 by Elionora Arnold,S.M. Gusein-Zade,Alexander N. Varchenko Pdf

​​​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.

Author : Elionora Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher : Birkhäuser
Page : 492 pages
File Size : 55,7 Mb
Release : 2012-05-17
Category : Mathematics
ISBN : 0817683429

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Singularities of Differentiable Maps, Volume 2 by Elionora Arnold,S.M. Gusein-Zade,Alexander N. Varchenko Pdf

​​​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.

Author : Vladimir Igorevich Arnolʹd
Publisher : Unknown
Page : 382 pages
File Size : 54,7 Mb
Release : 1985
Category : Differentiable mappings
ISBN : 3764331879

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Singularities of differentiable maps by Vladimir Igorevich Arnolʹd Pdf

Author : Vladimir Igorevich Arnolʹd
Publisher : Unknown
Page : 0 pages
File Size : 54,5 Mb
Release : 1988
Category : Differentiable mappings
ISBN : OCLC:471858323

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Singularities of Differentiable Maps by Vladimir Igorevich Arnolʹd Pdf

Author : Denis Ch‚niot
Publisher : World Scientific
Page : 1083 pages
File Size : 40,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812704108

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Singularity Theory by Denis Ch‚niot Pdf

The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 2024-05-05
Category : Electronic
ISBN : 9789814476393

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Singularity Theory by Anonim Pdf

Author : Victor Goryunov,Kevin Houston,Roberta Wik-Atique
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 53,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853597

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Real and Complex Singularities by Victor Goryunov,Kevin Houston,Roberta Wik-Atique Pdf

"This volume is a collection of papers presented at the 11th International Workshop on Real and Complex Singularities, held July 26-30, 2010, in Säao Carlos, Brazil, in honor of David Mond's 60th birthday. This volume reflects the high level of the conference discussing the most recent results and applications of singularity theory. Articles in the first part cover pure singularity theory: invariants, classification theory, and Milnor fibres. Articles in the second part cover singularities in topology and differential geometry, as well as algebraic geometry and bifurcation theory: Artin-Greenberg function of a plane curve singularity, metric theory of singularities, symplectic singularities, cobordisms of fold maps, Goursat distributions, sections of analytic varieties, Vassiliev invariants, projections of hypersurfaces, and linearity of the Jacobian ideal."--P. [4] of cover.

Author : Vladimir Igorevich Arnolʹd,Vladimir I. Arnol'd
Publisher : Unknown
Page : 0 pages
File Size : 43,8 Mb
Release : 1988
Category : Differentiable mappings
ISBN : 3764331852

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Singularities of Differentiable Maps by Vladimir Igorevich Arnolʹd,Vladimir I. Arnol'd Pdf

Author : Walter Neumann,Anne Pichon
Publisher : Springer Nature
Page : 356 pages
File Size : 43,7 Mb
Release : 2021-01-11
Category : Mathematics
ISBN : 9783030618070

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Introduction to Lipschitz Geometry of Singularities by Walter Neumann,Anne Pichon Pdf

This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.