Bifurcation And Symmetry

Author : Jorge Buescu,Paulo M.S.T. de Castro,Ana Paula Dias,Isabel S. Labouriau
Publisher : Birkhäuser
Page : 215 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879828

Get Book

Bifurcation, Symmetry and Patterns by Jorge Buescu,Paulo M.S.T. de Castro,Ana Paula Dias,Isabel S. Labouriau Pdf

The latest developments on both the theory and applications of bifurcations with symmetry. The text includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.

Author : BÖHMER,ALLGOWER,GOLUBITSKY
Publisher : Birkhäuser
Page : 323 pages
File Size : 40,9 Mb
Release : 2013-03-08
Category : Science
ISBN : 9783034875363

Get Book

Bifurcation and Symmetry by BÖHMER,ALLGOWER,GOLUBITSKY Pdf

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.

Author : Bernold Fiedler
Publisher : Springer
Page : 151 pages
File Size : 47,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391500

Get Book

Global Bifurcation of Periodic Solutions with Symmetry by Bernold Fiedler Pdf

This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.

Author : Pascal Chossat
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401109567

Get Book

Dynamics, Bifurcation and Symmetry by Pascal Chossat Pdf

This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.

Author : Martin Golubitsky,David G. Schaeffer
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 46,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461250340

Get Book

Singularities and Groups in Bifurcation Theory by Martin Golubitsky,David G. Schaeffer Pdf

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.

Author : Eugene L. Allgower,Klaus Böhmer,Martin Golubitsky
Publisher : Birkhauser
Page : 327 pages
File Size : 46,9 Mb
Release : 1992
Category : Mathematics
ISBN : 0817627391

Get Book

Bifurcation and Symmetry by Eugene L. Allgower,Klaus Böhmer,Martin Golubitsky Pdf

Author : Michael J. Field
Publisher : CRC Press
Page : 168 pages
File Size : 43,5 Mb
Release : 2020-02-17
Category : Mathematics
ISBN : 9781000657753

Get Book

Lectures on Bifurcations, Dynamics and Symmetry by Michael J. Field Pdf

This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. This text covers a wide range of current results in the subject of bifurcations, dynamics and symmetry. The style and format of the original lectures has largely been maintained and the notes include over 70 exercises.

Author : Michael J. Field
Publisher : CRC Press
Page : 172 pages
File Size : 40,5 Mb
Release : 2020-02-17
Category : Mathematics
ISBN : 9781000673470

Get Book

Lectures on Bifurcations, Dynamics and Symmetry by Michael J. Field Pdf

This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. This text covers a wide range of current results in the subject of bifurcations, dynamics and symmetry. The style and format of the original lectures has largely been maintained and the notes include over 70 exercises.

Author : Martin Golubitsky,Ian Stewart
Publisher : Birkhäuser
Page : 338 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783034881678

Get Book

The Symmetry Perspective by Martin Golubitsky,Ian Stewart Pdf

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

Author : Pascal Chossat
Publisher : Unknown
Page : 378 pages
File Size : 50,6 Mb
Release : 1994-07-31
Category : Electronic
ISBN : 9401109575

Get Book

Dynamics, Bifurcation and Symmetry by Pascal Chossat Pdf

Author : A. Vanderbauwhede
Publisher : Unknown
Page : 368 pages
File Size : 44,9 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:39015049317822

Get Book

Local Bifurcation and Symmetry by A. Vanderbauwhede Pdf

Author : Visarath In,Antonio Palacios
Publisher : Springer
Page : 406 pages
File Size : 49,9 Mb
Release : 2017-09-05
Category : Technology & Engineering
ISBN : 9783662555453

Get Book

Symmetry in Complex Network Systems by Visarath In,Antonio Palacios Pdf

This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.

Author : Shangjiang Guo,Jianhong Wu
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 41,7 Mb
Release : 2013-07-30
Category : Mathematics
ISBN : 9781461469926

Get Book

Bifurcation Theory of Functional Differential Equations by Shangjiang Guo,Jianhong Wu Pdf

This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

Author : David H. Sattinger
Publisher : SIAM
Page : 80 pages
File Size : 44,8 Mb
Release : 1983-01-01
Category : Mathematics
ISBN : 1611970296

Get Book

Branching in the Presence of Symmetry by David H. Sattinger Pdf

A discussion of developments in the field of bifurcation theory, with emphasis on symmetry breaking and its interrelationship with singularity theory. The notions of universal solutions, symmetry breaking, and unfolding of singularities are discussed in detail. The book not only reviews recent mathematical developments but also provides a stimulus for further research in the field.

Author : Mike Field
Publisher : World Scientific
Page : 493 pages
File Size : 53,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9781860948282

Get Book

Dynamics and Symmetry by Mike Field Pdf

This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems.This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G-manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone.