Differential Dynamical Systems Introduction

Author: Zhang Jinyan
Publisher:
Publish Date: 2001-03-01
Features: Dynamical systems organically combine rich physical content with the abstract methods of modern mathematics, serving as the mathematical form of classical mechanics. This book explains the basic contents of differential dynamical systems in an accessible manner, primarily studying the dynamical properties and structural stability of diffeomorphisms on their invariant sets. The book consists of eight chapters, covering topics such as: structural stability and hyperbolicity, the Smale horseshoe theorem and structural stability, the Hartman theorem and stable manifold theorem, structural stability of Morse-Smale vector fields, Markov partitions, and the omega-stability of axiom A. The perspectives and argumentation methods adopted in this book are designed to guide readers into this field from a relatively elementary level. Therefore, it provides a suitable reading material for readers preparing to enter this mathematical field for research. The book can serve as a graduate textbook for mathematics majors in higher education institutions and can also be referenced by faculty and researchers in science and engineering disciplines.