Singularities Of Differentiable Maps Volume 1
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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.
... 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).
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
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Author : V.I. Arnold
language : en
Publisher: Birkhäuser
Release Date : 2011-12-06
Singularities Of Differentiable Maps written by V.I. Arnold and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-06 with Mathematics categories.
... 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).
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 Critical point theory (Mathematical analysis) categories.
Singularities Of Differentiable Maps Volume 2
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Author : Elionora Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-16
Singularities Of Differentiable Maps Volume 2 written by Elionora 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 2012-05-16 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.
Singularities Of Differentiable Maps
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Author : V.I. Arnold
language : en
Publisher: Birkhäuser
Release Date : 1988-10-01
Singularities Of Differentiable Maps written by V.I. Arnold and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-01 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.
High Energy Physics And Cosmology Proceedings Of The 1990 Summer School
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Author : Jogesh C Pati
language : en
Publisher: #N/A
Release Date : 1991-05-16
High Energy Physics And Cosmology Proceedings Of The 1990 Summer School written by Jogesh C Pati and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-05-16 with categories.
This School presented topics of current interest in high energy physics including Superstrings, Unified Theories and Cosmology.
Singularities Algebraic Geometry Commutative Algebra And Related Topics
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Author : Gert-Martin Greuel
language : en
Publisher: Springer
Release Date : 2018-09-18
Singularities Algebraic Geometry Commutative Algebra And Related Topics written by Gert-Martin Greuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-18 with Mathematics categories.
This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.
The Mathematical Legacy Of Victor Lomonosov
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Author : Richard M. Aron
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-08-10
The Mathematical Legacy Of Victor Lomonosov written by Richard M. Aron and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-10 with Mathematics categories.
The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside’s theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.