Integrability of Dynamical Systems: Algebra and Analysis

  • Xiang Zhang

Part of the Developments in Mathematics book series (DEVM, volume 47)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Xiang Zhang
    Pages 89-148
  3. Back Matter
    Pages 353-380

About this book


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 center—focus 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.


integrability Jacobian multipliers Darboux integrability Liouvillian integrability Darboux polynomials Local integrability

Authors and affiliations

  • Xiang Zhang
    • 1
  1. 1.School of Mathematical ScienceShanghai Jiao Tong University ShanghaiChina

Bibliographic information