Stable Mappings and Their Singularities PDF Download

Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Stable Mappings and Their Singularities PDF full book. Access full book title Stable Mappings and Their Singularities by M. Golubitsky. Download full books in PDF and EPUB format.

Stable Mappings and Their Singularities

Stable Mappings and Their Singularities PDF Author: M. Golubitsky
Publisher: Springer Science & Business Media
ISBN: 146157904X
Category : Mathematics
Languages : en
Pages : 220

Book Description
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.

Stable Mappings and Their Singularities

Stable Mappings and Their Singularities PDF Author: M. Golubitsky
Publisher: Springer Science & Business Media
ISBN: 146157904X
Category : Mathematics
Languages : en
Pages : 220

Book Description
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.

Stable Mappings and Their Singularities

Stable Mappings and Their Singularities PDF Author: Martin Golubitsky
Publisher:
ISBN: 9787506200448
Category : Differentiable mappings
Languages : en
Pages : 209

Book Description


Stable Mappings and Their Singularities [By] M. Golubitsky [And] V. Guillemin

Stable Mappings and Their Singularities [By] M. Golubitsky [And] V. Guillemin PDF Author: Martin Golubitsky
Publisher:
ISBN:
Category : Differentiable mappings
Languages : en
Pages : 209

Book Description


Singularities of Mappings

Singularities of Mappings PDF Author: David Mond
Publisher: Springer Nature
ISBN: 3030344401
Category : Mathematics
Languages : en
Pages : 567

Book Description
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.

Singularities of Differentiable Maps

Singularities of Differentiable Maps PDF Author: V.I. Arnold
Publisher: Springer Science & Business Media
ISBN: 1461251540
Category : Mathematics
Languages : en
Pages : 390

Book Description
... 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).

Real Analytic and Algebraic Singularities

Real Analytic and Algebraic Singularities PDF Author: Toshisumi Fukui
Publisher: CRC Press
ISBN: 9780582328747
Category : Mathematics
Languages : en
Pages : 236

Book Description
This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.

Singularity Theory: Dedicated To Jean-paul Brasselet On His 60th Birthday - Proceedings Of The 2005 Marseille Singularity School And Conference

Singularity Theory: Dedicated To Jean-paul Brasselet On His 60th Birthday - Proceedings Of The 2005 Marseille Singularity School And Conference PDF Author: Jean-paul Brasselet
Publisher: World Scientific
ISBN: 9814476390
Category : Mathematics
Languages : en
Pages : 1083

Book Description
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.

Topological Stability of Smooth Mappings

Topological Stability of Smooth Mappings PDF Author: C.G. Gibson
Publisher: Springer
ISBN: 3540379576
Category : Mathematics
Languages : en
Pages : 160

Book Description
During the academic year 1974-75, the Department of Pure Mathematics in the University of Liverpool held a seminar on the topological stability of smooth mappings. The main objective was to piece together a complete proof of the topological stability theorem (conjectured by René Thom in 1960, and proved by John Mather in 1970) for which no published accounts existed. This volume comprises a write-up of the seminar by four of the participants. Any mathematician working in this area is conscious of a debt to the inventiveness of Thom, and to Mather for the technical work which placed much that was conjecture on firm mathematical foundations. The proof presented in these notes follows Thom's indications closely, and requires no more than some familiarity with differential topology and commutative algebra of the reader.

Singularities and Foliations. Geometry, Topology and Applications

Singularities and Foliations. Geometry, Topology and Applications PDF Author: Raimundo Nonato Araújo dos Santos
Publisher: Springer
ISBN: 3319736396
Category : Mathematics
Languages : en
Pages : 552

Book Description
This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

New Developments in Singularity Theory

New Developments in Singularity Theory PDF Author: Dirk Wiersma
Publisher: Springer Science & Business Media
ISBN: 9401008345
Category : Mathematics
Languages : en
Pages : 470

Book Description
Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.