This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the centerfocus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology.

Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.

Equips the reader with an understanding of integrability Summarizes the classical results of Darboux integrability and its modern development Connects analysis, algebraic geometry, field extension, differential form, Lie symmetry and normal form theory Includes supplementary material: sn.pub/extras

Autorentext
Xiang Zhang is a distinguished professor of Shanghai Jiao Tong University, China. He obtained his PhD degree in 1997 from Nanjing University, China.His main interest is in the field of qualitative theory, bifurcation theory and the theory of integrability of Ordinary Differential Equations and Dynamical Systems.

Inhalt
The fundamentals of the theory of integrability of differential systems.- The fundamentals of the theory of integrability of differential systems.- The fundamentals of the theory of integrability of differential systems.- Existence and degree of Darboux polynomials.- Algebraic, analytic and meromorphic integrability.- Applications of the Darboux theory of integrability.- Local integrability of differential systems.- Index.