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Stable Mappings And Their Singularities By M Golubitsky And V Guillemin
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Book Synopsis Stable Mappings and Their Singularities by : M. Golubitsky
Download or read book Stable Mappings and Their Singularities written by M. Golubitsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Nonlinear Analysis II by : Michele Matzeu
Download or read book Topological Nonlinear Analysis II written by Michele Matzeu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, ... mN, described in cartesian co ordinates by the system of equations (0.1) where f) V'k,m == -£l--' m = 1, 2, 3.
Book Synopsis Singularity Theory: Dedicated To Jean-paul Brasselet On His 60th Birthday - Proceedings Of The 2005 Marseille Singularity School And Conference by : Jean-paul Brasselet
Download or read book Singularity Theory: Dedicated To Jean-paul Brasselet On His 60th Birthday - Proceedings Of The 2005 Marseille Singularity School And Conference written by Jean-paul Brasselet and published by World Scientific. This book was released on 2007-02-08 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures On Dynamical Systems, Structural Stability And Their Applications by : Kotik K Lee
Download or read book Lectures On Dynamical Systems, Structural Stability And Their Applications written by Kotik K Lee and published by World Scientific. This book was released on 1992-05-14 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Book Synopsis Medial/Skeletal Linking Structures for Multi-Region Configurations by : James Damon
Download or read book Medial/Skeletal Linking Structures for Multi-Region Configurations written by James Damon and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions in which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries in a generic way. They introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the “positional geometry” of the collection. The linking structure extends in a minimal way the individual “skeletal structures” on each of the regions. This allows the authors to significantly extend the mathematical methods introduced for single regions to the configuration of regions.
Book Synopsis Theory of Singularities and Its Applications by : Vladimir Igorevich Arnolʹd
Download or read book Theory of Singularities and Its Applications written by Vladimir Igorevich Arnolʹd and published by American Mathematical Soc.. This book was released on 1990 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers such topics as construction of new knot invariants, stable cohomology of complementary spaces to diffusion diagrams, topological properties of spaces of Legendre maps, application of Weierstrass bifurcation points in projective curve flattenings, classification of singularities of projective surfaces with boundary, and control theory.
Book Synopsis Bifurcations in Hamiltonian Systems by : Henk Broer
Download or read book Bifurcations in Hamiltonian Systems written by Henk Broer and published by Springer. This book was released on 2003-01-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.
Book Synopsis Real and Complex Singularities by : M. Manoel
Download or read book Real and Complex Singularities written by M. Manoel and published by Cambridge University Press. This book was released on 2010-10-07 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to topics in both pure and applied mathematics. This volume brings together surveys and recent work from the tenth São Carlos meeting.
Book Synopsis Structural Stability, the Theory of Catastrophes, and Applications in the Sciences by : P. Hilton
Download or read book Structural Stability, the Theory of Catastrophes, and Applications in the Sciences written by P. Hilton and published by Springer. This book was released on 2006-11-14 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a progress report on an experimental program, begun a year ago, in the exploration of resonant furcations (= catastrophes) by analog simulation and direct observation - the macroscope program.
Book Synopsis Functions of Several Complex Variables and Their Singularities by : Wolfgang Ebeling
Download or read book Functions of Several Complex Variables and Their Singularities written by Wolfgang Ebeling and published by American Mathematical Soc.. This book was released on 2007 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.
Download or read book Image Understanding Workshop written by and published by . This book was released on 1990 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singularity Theory by : Denis Chniot
Download or read book Singularity Theory written by Denis Chniot and published by World Scientific. This book was released on 2007 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential Geometry Of Curves And Surfaces With Singularities by : Masaaki Umehara
Download or read book Differential Geometry Of Curves And Surfaces With Singularities written by Masaaki Umehara and published by World Scientific. This book was released on 2021-11-29 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields — singularity theory and differential geometry.The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space. In particular, by presenting the singular curvature, which originated through research by the authors, the Gauss-Bonnet theorem for surfaces is generalized to those with singularities. The Gauss-Bonnet theorem is intrinsic in nature, that is, it is a theorem not only for surfaces but also for 2-dimensional Riemannian manifolds. The book also elucidates the notion of Riemannian manifolds with singularities.These topics, as well as elementary descriptions of proofs of the recognition theorems, cannot be found in other books. Explicit examples and models are provided in abundance, along with insightful explanations of the underlying theory as well. Numerous figures and exercise problems are given, becoming strong aids in developing an understanding of the material.Readers will gain from this text a unique introduction to the singularities of curves and surfaces from the viewpoint of differential geometry, and it will be a useful guide for students and researchers interested in this subject.
Book Synopsis A Mathematical Approach to Research Problems of Science and Technology by : Ryuei Nishii
Download or read book A Mathematical Approach to Research Problems of Science and Technology written by Ryuei Nishii and published by Springer. This book was released on 2014-07-14 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.
Book Synopsis Recent Advances in Diffeologies and Their Applications by : Jean-Pierre Magnot
Download or read book Recent Advances in Diffeologies and Their Applications written by Jean-Pierre Magnot and published by American Mathematical Society. This book was released on 2024-02-02 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.
Book Synopsis New Developments in Differential Geometry by : L. Tamássy
Download or read book New Developments in Differential Geometry written by L. Tamássy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Colloquium on Differential Geometry, Debrecen, Hungary, July 26-30, 1994
Book Synopsis Nonlinear Functional Analysis and Its Applications, Part 1 by : Felix E. Browder
Download or read book Nonlinear Functional Analysis and Its Applications, Part 1 written by Felix E. Browder and published by American Mathematical Soc.. This book was released on 1986 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
