| 书目名称 | Nonlinear Differential Equations and Dynamical Systems | | 编辑 | Ferdinand Verhulst | | 视频video | | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | On the subject of differential equations a great many elementary books have been written. This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincaré. The global direct method is then discussed. To obtain more quantitative information the Poincaré-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions). The book presents the subject material from both the qualitative and the quantitative point of view. There are many examples to illustrate the theory and the reader should be able to start doing research | | 出版日期 | Textbook 19901st edition | | 关键词 | Implicit function; averaging methods; bifurcation theory; chaos; differential equation; differential equa | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-97149-5 | | isbn_ebook | 978-3-642-97149-5Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer-Verlag Berlin Heidelberg 1990 |
The information of publication is updating
|
|
发表于 2025-3-21 19:52:52
