| 书目名称 | Nonlinear Differential Equations and Dynamical Systems |
| 编辑 | Ferdinand Verhulst |
| 视频video | |
| 概述 | Includes supplementary material: |
| 丛书名称 | Universitext |
| 图书封面 |  |
| 描述 | On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. Stability theory is then developed starting with linearisation methods going back to Lyapunov and Poincaré. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincaré-Birkhoff theorem on periodicsolutions have been added. There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. The subj |
| 出版日期 | Textbook 1996Latest edition |
| 关键词 | Chaos; averaging methods; bifurcation theory; differential equations; dynamical systems; dynamische Syste |
| 版次 | 2 |
| doi | https://doi.org/10.1007/978-3-642-61453-8 |
| isbn_softcover | 978-3-540-60934-6 |
| isbn_ebook | 978-3-642-61453-8Series ISSN 0172-5939 Series E-ISSN 2191-6675 |
| issn_series | 0172-5939 |
| copyright | Springer-Verlag Berlin Heidelberg 1996 |
发表于 2025-3-21 16:20:18
