Differentiable Germs and Catastrophes

Author: Th Brocker,L. Lander

Publisher: Cambridge University Press

ISBN: 0521206812

Category: Mathematics

Page: 179

View: 5593

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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.
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Differentiable Germs and Catastrophes

Author: Th Brocker,L. Lander

Publisher: Cambridge University Press

ISBN: 0521206812

Category: Mathematics

Page: 179

View: 8972

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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.
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Handbook of Global Analysis

Author: Demeter Krupka,David Saunders

Publisher: Elsevier

ISBN: 9780080556734

Category: Mathematics

Page: 1244

View: 1322

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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
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Catastrophe Theory

Author: V. I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 364296799X

Category: Mathematics

Page: 79

View: 1768

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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 .
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Interaction Models

Author: Norman Biggs

Publisher: Cambridge University Press

ISBN: 0521217709

Category: Mathematics

Page: 101

View: 9786

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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.
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