GOLUBITSKY's Books

The Symmetry Perspective

From Equilibrium to Chaos in Phase Space and Physical Space

By: Martin Golubitsky,Ian Stewart

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The Symmetry Perspective

From Equilibrium to Chaos in Phase Space and Physical Space

By: Martin Golubitsky,Ian Stewart

The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS

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Page Count

338

Publisher

Birkhäuser

Published Date

ISBN 10

3034881673

ISBN 13

9783034881678

Fencing Is My Life

By: Sergei Golubitsky

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Fencing Is My Life

By: Sergei Golubitsky

The best fencing autobiography since Nadis, with inspiration and instruction for every fencer-a great gift for young fencers and an important story for coaches. In this book, a great champion tells his story and teaches his secrets Golubitsky, a four-time overall World Cup Champion, three-time World Champion, and winner of nineteen World Cups, recounts his difficult rise to the top, his triumphs and mistakes, and the lessons he learned from them. Sergei tells of his early days inside the old Soviet "sports machine," the breakup of the USSR, and his emergence into the new world of international fencing. This is an inspiring story of desire and persistence, frustration and triumph. Plus, its packed with practical tips for fencing and training. Numerous photos.

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ISBN 10

0965946894

ISBN 13

9780965946896

Stable Mappings and Their Singularities

By: M. Golubitsky,V. Guillemin

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Stable Mappings and Their Singularities

By: M. Golubitsky,V. Guillemin

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.

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Page Count

220

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146157904X

ISBN 13

9781461579045

Symmetry in Chaos

A Search for Pattern in Mathematics, Art, and Nature, Second Edition

By: Michael Field,Martin Golubitsky

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Symmetry in Chaos

A Search for Pattern in Mathematics, Art, and Nature, Second Edition

By: Michael Field,Martin Golubitsky

Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. 'Symmetry in Chaos' is an exploration of how combining seemingly contradictory principles can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics.

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Page Count

213

Publisher

SIAM

Published Date

ISBN 10

0898717701

ISBN 13

9780898717709

Differential Equations: A Dynamical Systems Approach

Higher-Dimensional Systems

By: John H. Hubbard,Beverly H. West

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Differential Equations: A Dynamical Systems Approach

Higher-Dimensional Systems

By: John H. Hubbard,Beverly H. West

This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as in the life sciences, physics, and economics. After an introduction, there follow chapters on systems of differential equations, of linear differential equations, and of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The whole is rounded off with an appendix containing important theorems from parts I and II, as well as answers to selected problems.

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Page Count

612

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461241928

ISBN 13

9781461241928

Singularities and Groups in Bifurcation Theory

Volume I

By: Martin Golubitsky,David G. Schaeffer

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Singularities and Groups in Bifurcation Theory

Volume I

By: Martin Golubitsky,David G. Schaeffer

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.

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Page Count

480

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146125034X

ISBN 13

9781461250340

Fearful Symmetry

Is God a Geometer?

By: Ian Stewart,Martin Golubitsky

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Fearful Symmetry

Is God a Geometer?

By: Ian Stewart,Martin Golubitsky

From the shapes of clouds to dewdrops on a spider's web, this accessible book employs the mathematical concepts of symmetry to portray fascinating facets of the physical and biological world. More than 120 figures illustrate the interaction of symmetry with dynamics and the mathematical unity of nature's patterns"--

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Page Count

326

Publisher

Courier Corporation

Published Date

ISBN 10

0486477584

ISBN 13

9780486477589

Pattern Formation in Continuous and Coupled Systems

A Survey Volume

By: Martin Golubitsky,Dan Luss,Steven H. Strogatz

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Pattern Formation in Continuous and Coupled Systems

A Survey Volume

By: Martin Golubitsky,Dan Luss,Steven H. Strogatz

Systems that generate new types of pattern such as discrete coupled systems, systems with global coupling, and combustion experiments were stressed, as were new types of pattern."--BOOK JACKET.

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354

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387988742

ISBN 13

9780387988740

Dynamics and Bifurcation in Networks

Theory and Applications of Coupled Differential Equations

By: Martin Golubitsky ,Ian Stewart

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Dynamics and Bifurcation in Networks

Theory and Applications of Coupled Differential Equations

By: Martin Golubitsky ,Ian Stewart

In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book’s main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of “admissible” ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions. This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.

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Page Count

867

Publisher

SIAM

Published Date

ISBN 10

1611977339

ISBN 13

9781611977332

Bifurcation and Symmetry

Cross Influence between Mathematics and Applications

By: BÖHMER,ALLGOWER,GOLUBITSKY

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Bifurcation and Symmetry

Cross Influence between Mathematics and Applications

By: BÖHMER,ALLGOWER,GOLUBITSKY

Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.

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Page Count

323

Publisher

Birkhäuser

Published Date

ISBN 10

3034875363

ISBN 13

9783034875363

Singularities and Groups in Bifurcation Theory

Volume II

By: Martin Golubitsky,Ian Stewart,David G. Schaeffer

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Singularities and Groups in Bifurcation Theory

Volume II

By: Martin Golubitsky,Ian Stewart,David G. Schaeffer

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.

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551

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461245745

ISBN 13

9781461245742

Multiparameter Bifurcation Theory

Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held July 14-20, 1985, with Support from the National Science Foundation

By: Martin Golubitsky,John Guckenheimer,American Mathematical Society

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Multiparameter Bifurcation Theory

Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held July 14-20, 1985, with Support from the National Science Foundation

By: Martin Golubitsky,John Guckenheimer,American Mathematical Society

This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature. The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.

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Page Count

408

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821850601

ISBN 13

9780821850602

Singularities and Groups in Bifurcation Theory

Volume I

By: Martin Golubitsky,David G. Schaeffer

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Singularities and Groups in Bifurcation Theory

Volume I

By: Martin Golubitsky,David G. Schaeffer

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Publisher

Springer

Published Date

ISBN 10

0387909990

ISBN 13

9780387909998

Book's by GOLUBITSKY

The Symmetry Perspective

The Symmetry Perspective

Fencing Is My Life

Fencing Is My Life

Stable Mappings and Their Singularities

Stable Mappings and Their Singularities

Symmetry in Chaos

Symmetry in Chaos

Differential Equations: A Dynamical Systems Approach

Differential Equations: A Dynamical Systems Approach

Singularities and Groups in Bifurcation Theory

Singularities and Groups in Bifurcation Theory

Fearful Symmetry

Fearful Symmetry

Pattern Formation in Continuous and Coupled Systems

Pattern Formation in Continuous and Coupled Systems

Dynamics and Bifurcation in Networks

Dynamics and Bifurcation in Networks

Bifurcation and Symmetry

Bifurcation and Symmetry

Singularities and Groups in Bifurcation Theory

Singularities and Groups in Bifurcation Theory

Multiparameter Bifurcation Theory

Multiparameter Bifurcation Theory

Singularities and Groups in Bifurcation Theory

Singularities and Groups in Bifurcation Theory

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