| Global Transversality, Resonance and Chaotic Dynamics Contributor(s): Luo, Albert C. J. (Author) |
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ISBN: 9812771115 ISBN-13: 9789812771117 Publisher: World Scientific Publishing Company OUR PRICE: $213.75 Product Type: Hardcover Published: April 2008 Annotation: Luo (Southern Illinois U. Edwardsville) presents a new theory for n-dimensional nonlinear dynamics. He presents the differential geometrical relations between two flows in two different dynamical systems through G-functions and then investigates the global transversality in nonlinear dynamical systems based on the G-functions. He discusses a theory for chaotic layer dynamics for nonlinear Hamiltonian systems, including the resonant theory of stochastic layers and the stochasticity of resonant layers. Nonlinear dynamics on the (2n-1)-dimensional equi-energy surface is also discussed, as is the stability and grazing bifurcations for dissipative nonlinear dynamical systems. Finally, switchability of a flow from a domain to an adjacent domain in discontinuous dynamical systems is discussed through the G-functions, and the first incremental increment for discontinuous dynamical systems are given. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General |
| Dewey: 003.857 |
| LCCN: 2008299311 |
| Physical Information: 460 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. |