Integrability of Dynamical Systems: Algebra and Analysis

Focusing on the fundamental theory of integrability, this book explores the development of ordinary differential equations, emphasizing Darboux theory. It presents classical and modern results of Darboux integrability, alongside related polynomials and their applications. Key topics include the reduction of Liouville integrability, the center-focus problem, the weakened Hilbert 16th problem regarding algebraic limit cycles, and global dynamical analysis in various fields such as physics, mechanics, and biology.