Singularity Theory I
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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
Introduction To Singularities And Deformations
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Author : Gert-Martin Greuel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-23
Introduction To Singularities And Deformations written by Gert-Martin Greuel 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 2007-02-23 with Mathematics categories.
Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.
Singularities And Groups In Bifurcation Theory
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Author : Martin Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Singularities And Groups In Bifurcation Theory written by Martin Golubitsky 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 2013-11-27 with Mathematics categories.
This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.
Introduction To Singularities
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Author : Shihoko Ishii
language : en
Publisher: Springer
Release Date : 2014-11-19
Introduction To Singularities written by Shihoko Ishii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.
Differential Geometry From A Singularity Theory Viewpoint
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Author : Shyuichi Izumiya
language : en
Publisher: World Scientific
Release Date : 2015-10-29
Differential Geometry From A Singularity Theory Viewpoint written by Shyuichi Izumiya and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-29 with Mathematics categories.
Differential Geometry from a 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 wavefronts. 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.
Singularity Theory And Gravitational Lensing
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Author : Arlie O. Petters
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularity Theory And Gravitational Lensing written by Arlie O. Petters 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 Science categories.
Astronomers do not do experiments. They observe the universe primarily through detect ing light emitted by stars and other luminous objects. Since this light must travel through space to reach us, variations in the metric of space affects the appearance of astronomical objects. These variations lead to dramatic changes in the shape and brightness of astronom ical sources. Because these variations are sensitive to mass rather than to light, observations of gravitational lensing enable astronomers to probe the mass distribution of the universe. With gravitational lensing observations, astronomers are addressing many of the most important scientific questions in astronomy and physics: • What is the universe made of? Most of the energy and mass in the universe is not in the form of luminous objects. Stars account for less than 1 % of the energy density of the universe. Perhaps, as much as another 3% of the energy density of the universe is in the form of warm gas that fills the space between galaxies. The remaining 96% of the energy density is in some yet unidentified form. Roughly one third of this energy density of the universe is "dark matter," matter that clusters gravitationally but does not emit light. Most cosmologists suspect that this dark matter is composed of weakly interacting subatomic particles. However, most of the energy density of the universe appears to be in an even stranger form: energy associated with empty space.
Singularity Theory And An Introduction To Catastrophe Theory
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Author : Yung-Chen Lu
language : en
Publisher:
Release Date : 1980
Singularity Theory And An Introduction To Catastrophe Theory written by Yung-Chen Lu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Singularity Theory
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Author : V. I. Arnold
language : en
Publisher: Cambridge University Press
Release Date : 1981-09-17
Singularity Theory written by V. I. Arnold and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-09-17 with History categories.
Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis. In this volume are collected seven of his survey articles from Russian Mathematical Surveys on singularity theory, the area to which he has made most contribution. These surveys contain Arnold's own analysis and synthesis of a decade's work. All those interested in singularity theory will find this an invaluable compilation. Professor C. T. C. Wall has written an introduction outlining the significance and content of the articles.
Theory Of Singularities And Its Applications
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Theory Of Singularities And Its Applications written by Vladimir Igorevich Arnolʹd and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Handbook Of Geometry And Topology Of Singularities I
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Author : José Luis Cisneros Molina
language : en
Publisher: Springer Nature
Release Date : 2020-10-24
Handbook Of Geometry And Topology Of Singularities I written by José Luis Cisneros Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-24 with Mathematics categories.
This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.