非线性物理科学：连续动力系统（英文版）

Nonlinear Physical Science: Continuous Dynamical Systems (English Version) is a highly innovative work that presents the first analytical representation of chaos in dynamical systems. The book introduces a new, clear, and succinct perspective on the stability and bifurcation theory of continuous dynamical systems, which assists readers in better understanding the regularity and complexity inherent in dynamical systems. It begins by analyzing analytical solutions for linear continuous systems with multiple characteristic roots and their stability, followed by a detailed discussion of the stability and singularity classification of nonlinear continuous dynamical systems. The book then systematically examines the analytical path from oscillatory solutions to chaos in dynamical systems. Additionally, it analyzes the global transversality of flows in dynamical systems with coexisting or non-coexisting orbits and provides an analytical criterion for chaos in nonlinear Hamiltonian systems, thereby enabling better understanding of the physical mechanisms of chaos in nonlinear dynamical systems. This book serves as a valuable reference for undergraduate students majoring in applied mathematics, physics, mechanics, and control as well as professors and researchers in these fields. Author Chaoujun Luo is an internationally renowned expert in nonlinear dynamical systems and mechanics, and a tenured professor at Southern Illinois University Edwardsville. His primary research interests include chaos in nonlinear Hamiltonian systems, nonlinear mechanics, and discontinuous dynamical systems.