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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences, 42),New
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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 nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined twodimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors.' #Book Review Engineering Societies Library, New York#1 'An attempt to make research tools concerning strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations.' #American Mathematical Monthly#2
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- Q: What topics are covered in 'Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields'? A: This book covers methods from dynamical systems and bifurcation theories, focusing on nonlinear oscillations, local bifurcation theory, analytical methods, and global bifurcations, among other advanced topics.
- Q: Who is the author of this book? A: The book is authored by John Guckenheimer, a noted researcher in the field of applied mathematics.
- Q: What is the publication date of this book? A: The book was published on August 1, 1983.
- Q: What type of binding does this book have? A: This book has a hardcover binding, which is durable and suitable for long-term use.
- Q: How many pages are in the book? A: The book contains a total of 478 pages.
- Q: Is this book suitable for beginners in the field of dynamical systems? A: This book assumes a foundational understanding of mathematical concepts, making it more suitable for advanced students or professionals rather than complete beginners.
- Q: What is the condition of the book being sold? A: The book is listed as 'New', indicating it has not been previously used.
- Q: What category does this book fall under? A: The book falls under the category of Differential Equations.
- Q: Are there any reviews or endorsements from professionals in the field? A: Yes, the book has received positive reviews highlighting its contributions to research tools in dynamical systems and its clear presentation of complex topics.
- Q: Does the book include practical examples or applications? A: Yes, the book provides practical examples from nonlinear oscillations and discusses applications that demonstrate theoretical concepts.