Singularities Of Differentiable Maps

Author : V.I. Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 50,7 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780817683405

Get Book

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 : V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251545

Get Book

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 : Elionora Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 46,9 Mb
Release : 2012-05-16
Category : Mathematics
ISBN : 9780817683436

Get Book

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 Igorevič Arnol'd
Publisher : Unknown
Page : 0 pages
File Size : 47,8 Mb
Release : 2012
Category : Electronic
ISBN : OCLC:922676508

Get Book

Singularities of Differentiable Maps by Vladimir Igorevič Arnol'd Pdf

Author : Elionora Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher : Birkhäuser
Page : 492 pages
File Size : 41,5 Mb
Release : 2012-05-17
Category : Mathematics
ISBN : 0817683429

Get Book

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,Sabir Medzhidovich Guseĭn-Zade,Aleksandr Nikolaevich Varchenko
Publisher : Unknown
Page : 492 pages
File Size : 51,7 Mb
Release : 1988
Category : Critical point theory (Mathematical analysis)
ISBN : 3764331852

Get Book

Singularities of Differentiable Maps by Vladimir Igorevich Arnolʹd,Sabir Medzhidovich Guseĭn-Zade,Aleksandr Nikolaevich Varchenko Pdf

Author : Vladimir Igorevich Arnolʹd
Publisher : Unknown
Page : 0 pages
File Size : 40,9 Mb
Release : 1988
Category : Differentiable mappings
ISBN : OCLC:471858323

Get Book

Singularities of Differentiable Maps by Vladimir Igorevich Arnolʹd Pdf

Author : V.I. Arnold,Alexander Varchenko,S.M. Gusein-Zade
Publisher : Birkhäuser
Page : 396 pages
File Size : 47,8 Mb
Release : 2011-12-06
Category : Mathematics
ISBN : 1461251559

Get Book

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 : Birkhäuser
Page : 492 pages
File Size : 41,6 Mb
Release : 2012-02-22
Category : Mathematics
ISBN : 1461239419

Get Book

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 Igorevič Arnolʹd,Sabir Medžidovič Gusejn-Zade,Aleksandr Nikolaevič Varchenko
Publisher : Unknown
Page : 128 pages
File Size : 45,5 Mb
Release : 2012
Category : Differentiable mappings
ISBN : OCLC:834456116

Get Book

Singularities of Differentiable Maps by Vladimir Igorevič Arnolʹd,Sabir Medžidovič Gusejn-Zade,Aleksandr Nikolaevič Varchenko Pdf

Author : Vladimir Igorevich Arnolʹd,Vladimir I. Arnol'd
Publisher : Unknown
Page : 0 pages
File Size : 55,9 Mb
Release : 1988
Category : Differentiable mappings
ISBN : 3764331852

Get Book

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

Author : Vladimir Igorevich Arnolʹd
Publisher : Unknown
Page : 382 pages
File Size : 43,7 Mb
Release : 1985
Category : Differentiable mappings
ISBN : 3764331879

Get Book

Singularities of differentiable maps by Vladimir Igorevich Arnolʹd Pdf

Author : Vladimir I. Arnol'd
Publisher : Unknown
Page : 382 pages
File Size : 45,6 Mb
Release : 1985
Category : Electronic
ISBN : 3764331879

Get Book

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

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 53,8 Mb
Release : 1988
Category : Differentiable mappings
ISBN : OCLC:873979566

Get Book

Singularities of Differentiable Maps by Anonim Pdf

Author : Osamu Saeki
Publisher : Springer
Page : 154 pages
File Size : 45,8 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9783540446484

Get Book

Topology of Singular Fibers of Differentiable Maps by Osamu Saeki Pdf

The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.