Methods In Equivariant Bifurcations And Dynamical Systems
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Methods In Equivariant Bifurcations And Dynamical Systems
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Author : Pascal Chossat
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2000
Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This invaluable book presents the state-of-the-art in equivariant bifurcation and dynamical systems theory, with a special emphasis on the computational aspects, PDE's and applications. This theory provides powerful tools for the analysis of spontaneous symmetry-breaking phenomena, in space as well as in time. Examples of applications from various areas of science are provided and analyzed.
Methods In Equivariant Bifurcations And Dynamical Systems
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Author : Pascal Chossat
language : en
Publisher:
Release Date : 2000
Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Methods In Equivariant Bifurcations And Dynamical Systems
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Author : Pascal Chossat
language : en
Publisher: World Scientific Publishing Company
Release Date : 2000-02-28
Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-28 with Science categories.
This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.
Numerical Methods For Bifurcations Of Dynamical Equilibria
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Author : Willy J. F. Govaerts
language : en
Publisher: SIAM
Release Date : 2000-01-01
Numerical Methods For Bifurcations Of Dynamical Equilibria written by Willy J. F. Govaerts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems
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Author : Mariana Haragus
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems written by Mariana Haragus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.
An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Computer Algebra Methods For Equivariant Dynamical Systems
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Author : Karin Gatermann
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 2000-03-27
Computer Algebra Methods For Equivariant Dynamical Systems written by Karin Gatermann and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-27 with Computers categories.
This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research. Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.
Elements Of Applied Bifurcation Theory
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Author : Yuri Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-29
Elements Of Applied Bifurcation Theory written by Yuri Kuznetsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-29 with Mathematics categories.
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Numerical Continuation Methods For Dynamical Systems
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Author : Bernd Krauskopf
language : en
Publisher: Springer
Release Date : 2007-11-06
Numerical Continuation Methods For Dynamical Systems written by Bernd Krauskopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-06 with Science categories.
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Rayleigh B Nard Convection
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Author : Alexander V. Getling
language : en
Publisher: World Scientific
Release Date : 1998
Rayleigh B Nard Convection written by Alexander V. Getling and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
This invaluable book presents a concise but systematic account of the formation of spatial flow structures in a horizontal fluid layer heated from below. Flows of this type, known as Rayleigh-Bnard convection, show important features of behaviour inherent not only in various hydrodynamic-instability phenomena but also in nonlinear pattern-forming processes in other contexts. The book describes the basic methods of investigating convection patterns, and the types of two- and three-dimensional flows, pattern defects, and sequences of convection-regime changes.The author pays special attention to the question of how various factors (mainly reducible to initial and boundary conditions) determine the shapes and sizes of the structures which develop. In this way, the role of order and disorder in flow patterns, as a factor strongly affecting the character of the evolution of structures, is revealed. The presentation emphasizes the physical picture of these phenomena, without excessive mathematical detail.
Computational Methods For The Atmosphere And The Oceans
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Author : Roger Temam
language : en
Publisher: Elsevier
Release Date : 2009-06-16
Computational Methods For The Atmosphere And The Oceans written by Roger Temam and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-16 with Computers categories.
This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.• Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics • Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences• Contributions uniquely address central problems and provide a survey of the frontier of research