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Dynamics and Bifurcations
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Jack K Hale
The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications ...
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Groups and symmetry
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M. A. Armstrong
Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the ...
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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John Guckenheimer, Philip Holmes (Photographer), F John (Editor)
From the reviews: 'This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from ...
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Elements of Applied Bifurcation Theory
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Iu A Kuznetsov, Yuri A Kuznetsov
Presents nonlinear dynamical systems and their bifurcations. providing procedures and examples for the application of general mathematical results to particular problems. This book incorporates theoretical developments, in particular, and improved numerical methods for bifurcation analysis.
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Instabilities and Fronts in Extended Systems
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Pierre Collet, Jean-Pierre Eckmann
The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results ...
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Controlling Chaos and Bifurcations in Engineering Systems
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by
Guanrong Chen (Editor)
Over the last two decades, chaos in engineering systems has moved from being simply a curious phenomenon to one with real, practical significance and utility. Engineers, scientists, and mathematicians have similarly advanced from the passive role of analyzing chaos to their present, active role of controlling chaos-control directed not only at ...
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Imperfect Bifurcation in Structures and Materials
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Kiyohiro Ikeda, Kazuo Murota
This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods - based on asymptotic, probabilistic, and group-theoretic standpoints - are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes). Engineers may find this book, ...
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Normal Forms and Bifurcation of Planar Vector Fields
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Chow, Li, Wang
This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory ...
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Dynamical Systems V
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by
Vladimir I Arnol'd (Editor), R V Gamkrelidze (Editor), V S Aframojvich (Designer)
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such ...
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Bifurcation, Symmetry and Patterns
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by
Jorge Buescu
This book represents the latest developments on both the theory and applications of bifurcations with symmetry. It 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 ...
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Piecewise-Smooth Dynamical Systems: Theory and Applications
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by
Mario Di Bernardo, C J Budd, A R Champneys
Traditional analysis of dynamical systems has restricted its attention to smooth problems, but it has become increasingly clear that there are distinctive phenomena unique to discontinuous systems that can be analyzed mathematically but which fall outside the usual methodology for smooth dynamical systems. The primary purpose of this book is to ...
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Perturbation Methods, Bifurcation Theory, and Computer Algebra
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Richard Rand, D. Armbruster
Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the ...
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Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems
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by
U K Le, Vy Khoi Le, Klaus Schmitt
"Bifurcation Problems for Variational Inequalities" presents an up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and ...
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Singularities and Groups in Bifurcation Theory: Volume 1
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Martin Golubitsky, David G Schaeffer
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Global Bifurcations and Chaos: Analytical Methods
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S. Wiggins
"Global Bifurcations and Chaos: Analytical Methods" is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific ...
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Elementary Stability and Bifurcation Theory
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G. Ioos, D. D. Jospeh, D. D. Joseph
This second edition has been substantially revised. Its purpose is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. It is written not only for mathematicians, but for the broadest audience of potentially interested learners, including engineers, biologists, chemists, ...
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Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems
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by
Michel Demazure, David Chillingworth (Translator)
Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential ...
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Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations fractal dimensions and infinitely many attractors
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Palis, Takens
This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic ...
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Lectures on Bifurcations, Dynamics and Symmetry
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by
Michael Field
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. ...
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Global Bifurcation Theory and Hilbert's Sixteenth Problem
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Valery A Gaiko
This volume is devoted to the qualitative investigation of two-dimensional polynomial dynamical systems, and is aimed at solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The author presents a global bifurcation theory of such systems and suggests a new global approach to the study of limit cycle ...
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Singularities and Groups in Bifurcation Theory: Volume 2
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Martin Golubitsky, David G Schaeffer, Ian Stewart
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 ...
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Bifurcations of Planar Vector Fields
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by
Jean-Pierre Francoise (Editor), Robert Roussarie (Editor)
A collection of papers on differential equations and dynamical systems which stresses topics relating to Hilbert's 16th problem. Among these are a solution to Dulac's problem, results on the multiplicity of singular cycles and results on the zeroes of abelian integrals.
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Bifurcation Theory: An Introduction with Applications to Pdes
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Hansjorg Kielhofer, Hansjvrg Kielhvfer, Hansjc6rg Kielhc6fer
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for ...
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Bifurcation Analysis, Principles, Applications and Synthesis
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Michiel Hazewinkel, R Jurkovich (Editor), J H P Pealinck (Editor)
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Bifurcation Theory, Mechanics and Physics: Mathematical Developments and Applications
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by
Claude Paul Bruter, A Aragnol (Editor), A Lichnorowicz (Editor)
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