Singularities Of Smooth Maps
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Singularities Of Smooth Functions And Maps
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Author : J. Martinet
language : en
Publisher: CUP Archive
Release Date : 1982-08-19
Singularities Of Smooth Functions And Maps written by J. Martinet and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-08-19 with Mathematics categories.
Singularities Of Smooth Maps
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Author : James Eells
language : en
Publisher: Routledge
Release Date : 1967
Singularities Of Smooth Maps written by James Eells and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
Singularities Of Differentiable Maps
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 1985-01-01
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 1985-01-01 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 Mappings
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Author : David Mond
language : en
Publisher: Springer Nature
Release Date : 2020-01-23
Singularities Of Mappings written by David Mond and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.
The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
Singularity Theory I
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularity Theory I 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.
From the reviews: "... My general impression is of a particularly nice book, with a well-balanced bibliography, recommended!" Mededelingen van Het Wiskundig Genootschap, 1995 "... The authors offer here an up to date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader, a carefully prepared and extensive bibliography ... makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. ... Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis." European Mathematical Society Newsletter, 1994
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 Smooth Mappings With Additional Structures
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Author : V. I. Arnolʹd
language : en
Publisher:
Release Date : 1995
Singularities Of Smooth Mappings With Additional Structures written by V. I. Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mappings (Mathematics). categories.
Differential Geometry From A Singularity Theory Viewpoint
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Author : Shyuichi Izumiya
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2015
Differential Geometry From A Singularity Theory Viewpoint written by Shyuichi Izumiya and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
Differential Geometry from Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wave fronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.
Topology Of Singular Fibers Of Differentiable Maps
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Author : Osamu Saeki
language : en
Publisher: Springer
Release Date : 2004-08-30
Topology Of Singular Fibers Of Differentiable Maps written by Osamu Saeki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-30 with Mathematics categories.
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.
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).