Differentiable Germs and Catastrophes

Author: Th Brocker,L. Lander

Publisher: Cambridge University Press

ISBN: 0521206812

Category: Mathematics

Page: 179

View: 9912

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This book gives a fairly elementary introduction to the local theory of differentiable mappings and is suitable as a text for courses to graduates and advanced undergraduates.

Handbook of Global Analysis

Author: Demeter Krupka,David Saunders

Publisher: Elsevier

ISBN: 9780080556734

Category: Mathematics

Page: 1244

View: 6201

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This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents

Catastrophe Theory

Author: V. I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 364296799X

Category: Mathematics

Page: 79

View: 3077

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Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of by passing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bi bliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-con troversial results from the mathematical theories of singulari ties and bifurcation. The author has tried to explain the essence of the fundamen tal results and applications to readers having minimal mathe matical background but the reader is assumed to have an in quiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20 .

Differentiable Germs and Catastrophes

Author: Th Brocker,L. Lander

Publisher: Cambridge University Press

ISBN: 0521206812

Category: Mathematics

Page: 179

View: 1861

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This book gives a fairly elementary introduction to the local theory of differentiable mappings and is suitable as a text for courses to graduates and advanced undergraduates.

Catastrophe theory

Author: Domenico P. L. Castrigiano,Sandra A. Hayes

Publisher: Westview Pr

ISBN: 9780813341262

Category: Mathematics

Page: 264

View: 3527

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This edition contains complete proofs of Thomas classification theorems as well as the genericity and stability results assuming only elementary calculus and linear algebra. Catastrophe Theory is an intriguing beautiful theory whose striking feature is its universality. The text is self-contained and progressing in its approach. It is also unique in its treatment of genericity and stability.

General Systems

Author: Society for the Advancement of General Systems Theory,International Society for the Systems Sciences

Publisher: N.A

ISBN: N.A

Category: Social sciences

Page: N.A

View: 4794

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Interaction Models

Author: Norman Biggs

Publisher: Cambridge University Press

ISBN: 0521217709

Category: Mathematics

Page: 101

View: 7324

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This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.

Supersymmetry for Mathematicians

An Introduction

Author: V. S. Varadarajan

Publisher: American Mathematical Soc.

ISBN: 0821835742

Category: Mathematics

Page: 300

View: 2712

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Supersymmetry has been the object of study by theoretical physicists since the early 1970's. In recent years it has attracted the interest of mathematicians because of its novelty, and because of significance, both in mathematics and physics, of the main issues it raises. This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner. It begins with a brief introduction to the physical foundations of the theory, especially the classification of relativistic particles and their wave equations, such as the equations of Dirac and Weyl. It then continues the development of the theory of supermanifolds stressing the analogy with the Grothendieck theory of schemes. All the super linear algebra needed for the book is developed here and the basic theorems are established: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity.

Catastrophe Theory and Its Applications

Author: Tim Poston,Ian Stewart

Publisher: Courier Corporation

ISBN: 0486143783

Category: Mathematics

Page: 512

View: 6599

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First integrated treatment of main ideas behind René Thom's theory of catastrophes stresses detailed applications in the physical sciences. Mathematics of theory explained with a minimum of technicalities. Over 200 illustrations clarify text designed for researchers and postgraduate students in engineering, mathematics, physics and biology. 1978 edition. Bibliography.

Monographic Series

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category: Children's literature in series

Page: N.A

View: 4834

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Robust Chaos and Its Applications

Author: Elhadj Zeraoulia,Julien C. Sprott

Publisher: World Scientific

ISBN: 9814374075

Category: Mathematics

Page: 454

View: 661

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Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.

1089 and All that : a Journey Into Mathematics

Author: D. J. Acheson

Publisher: Oxford University Press, USA

ISBN: 9780198516231

Category: Mathematics

Page: 178

View: 2736

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This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famous cartoonists. This unusual book is one of the most readable explanations of mathematics available.