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Author: Dana Schlomiuk
Publisher: Springer Science & Business Media
ISBN: 9780792323921
Category : Mathematics
Languages : en
Pages : 500
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Book Description
The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.
Author: Dana Schlomiuk
Publisher: Springer Science & Business Media
ISBN: 9780792323921
Category : Mathematics
Languages : en
Pages : 500
Get Book Here
Book Description
The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.
Author: Dana Schlomiuk
Publisher: Springer Science & Business Media
ISBN: 9401582386
Category : Mathematics
Languages : en
Pages : 483
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Book Description
The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.
Author: David Ruelle
Publisher: Elsevier
ISBN: 1483272184
Category : Mathematics
Languages : en
Pages : 196
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Book Description
Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.
Author: Yuri Kuznetsov
Publisher: Springer Science & Business Media
ISBN: 1475739788
Category : Mathematics
Languages : en
Pages : 648
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Book Description
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.
Author: Jack K. Hale
Publisher: Springer Science & Business Media
ISBN: 1461244269
Category : Mathematics
Languages : en
Pages : 577
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Book Description
In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.
Author: John Guckenheimer
Publisher: Springer Science & Business Media
ISBN: 1461211409
Category : Mathematics
Languages : en
Pages : 475
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Book Description
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Author: Harry Dankowicz
Publisher: SIAM
ISBN: 1611972566
Category : Mathematics
Languages : en
Pages : 585
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Book Description
This book provides a comprehensive introduction to the mathematical methodology of parameter continuation. It develops a systematic formalism for constructing and implementing abstract representations of continuation problems with equal emphasis on theoretical rigor, algorithm development and software engineering. The book demonstrates the use of fully developed toolbox templates for boundary-value problems to the analysis of periodic orbits, quasi-periodic invariant tori, and connecting orbits between equilibria and/or periodic orbits. The book contains extensive and fully-worked examples that illustrate the application of the MATLAB-based Computational Continuation Core (COCO) to cutting-edge research in applied dynamical systems. Many exercises and open-ended projects on both theoretical and algorithmic aspects of the material are provided, suitable for self-study and course assignments. It is intended for students and teachers of nonlinear dynamics and engineering at the advanced undergraduate or first-year graduate level, as well as practitioners engaged in modeling dynamical systems or software development.
Author: Ale Jan Homburg
Publisher: American Mathematical Soc.
ISBN: 0821804413
Category : Mathematics
Languages : en
Pages : 143
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Book Description
In this book, the author investigates a class of smooth one parameter families of vector fields on some $n$-dimensional manifold, exhibiting a homoclinic bifurcation. That is, he considers generic families $x_\mu$, where $x_0$ has a distinguished hyperbolic singularity $p$ and a homoclinic orbit; an orbit converging to $p$ both for positive and negative time. It is assumed that this homoclinic orbit is of saddle-saddle type, characterized by the existence of well-defined directions along which it converges to the singularity $p$. The study is not confined to a small neighborhood of the homoclinic orbit. Instead, the position of the stable and unstable set of the homoclinic orbit is incorporated and it is shown that homoclinic bifurcations can lead to complicated bifurcations and dynamics, including phenomena like intermittency and annihilation of suspended horseshoes.
Author: Dirk Roose
Publisher: Springer Science & Business Media
ISBN: 9400906595
Category : Mathematics
Languages : en
Pages : 415
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Book Description
Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989
Author: John Guckenheimer
Publisher:
ISBN: 9781461211419
Category :
Languages : en
Pages : 484
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Book Description
