Singularities of Differentiable Maps - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Singularities of Differentiable Maps write by V.I. Arnold. This book was released on 2012-12-06. Singularities of Differentiable Maps available in PDF, EPUB and Kindle. ... 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
Singularities of Differentiable Maps, Volume 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Singularities of Differentiable Maps, Volume 1 write by V.I. Arnold. This book was released on 2012-05-24. Singularities of Differentiable Maps, Volume 1 available in PDF, EPUB and Kindle. 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, Volume 2
Singularities of Differentiable Maps, Volume 2 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Singularities of Differentiable Maps, Volume 2 write by Elionora Arnold. This book was released on 2012-05-16. Singularities of Differentiable Maps, Volume 2 available in PDF, EPUB and Kindle. 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.
Real and Complex Singularities
Real and Complex Singularities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Real and Complex Singularities write by Victor Goryunov. This book was released on 2012. Real and Complex Singularities available in PDF, EPUB and Kindle. "This volume is a collection of papers presented at the 11th International Workshop on Real and Complex Singularities, held July 26-30, 2010, in Sao Carlos, Brazil, in honor of David Mond's 60th birthday. This volume reflects the high level of the conference discussing the most recent results and applications of singularity theory. Articles in the first part cover pure singularity theory: invariants, classification theory, and Milnor fibres. Articles in the second part cover singularities in topology and differential geometry, as well as algebraic geometry and bifurcation theory: Artin-Greenberg function of a plane curve singularity, metric theory of singularities, symplectic singularities, cobordisms of fold maps, Goursat distributions, sections of analytic varieties, Vassiliev invariants, projections of hypersurfaces, and linearity of the Jacobian ideal."--P. [4] of cover.
Introduction to Lipschitz Geometry of Singularities
Introduction to Lipschitz Geometry of Singularities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Lipschitz Geometry of Singularities write by Walter Neumann. This book was released on 2021-01-11. Introduction to Lipschitz Geometry of Singularities available in PDF, EPUB and Kindle. This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.
