Methods of qualitative theory in nonlinear dynamics
著者
書誌事項
Methods of qualitative theory in nonlinear dynamics
（World Scientific series on nonlinear science / editor, Leon O. Chua, ser. A . Monographs and treatises ; v. 4-5）
World Scientific, c1998-2001
- pt. 1
- pt. 2
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注記
Includes bibliographical references and index
Other authors: Andrey L. Shilnikov, Dmitry V. Turaev, Leon O. Chua
内容説明・目次
内容説明
Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need.Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
目次
- Basic conepts
- structurally stable equilibrium states of dynamical systems
- structurally stable periodic trajectories of dynamical systems
- invariant tori
- centre manifold, local case
- centre manifold, non-local case.
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