Methods Of Qualitative Theory In Nonlinear Dynamics (Part I)

(Part I)

Leonid P Shilnikov, Andrey L Shilnikov, Dmitry V Turaev

• Publisher: World Scientific
• Year: 1998
• Print ISBN: 9789810233822, 9789810233822
• eBook ISBN: 9789812798596
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

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 Poincaré, 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.

Table of contents

• Contents
• Preface
• Chapter 1 BASIC CONCEPTS
• Chapter 2 STRUCTURALLY STABLE EQUILIBRIUM STATES OF DYNAMICAL SYSTEMS
• Chapter 3 STRUCTURALLY STABLE PERIODIC TRAJECTORIES OF DYNAMICAL SYSTEMS
• Chapter 4 INVARIANT TORI
• Chapter 5 CENTER MANIFOLD. LOCAL CASE
• Chapter 6 CENTER MANIFOLD. NON-LOCAL CASE
• Appendix A SPECIAL FORM OF SYSTEMS NEAR A SADDLE EQUILIBRIUM STATE
• Appendix B FIRST ORDER ASYMPTOTIC FOR THE TRAJECTORIES NEAR A SADDLE FIXED POINT
• Bibliography
• Index