Integrability of Dynamical Systems: Algebra and Analysis

✍ Scribed by Xiang Zhang (auth.)

• Publisher: Springer Singapore
• Year: 2017
• Tongue: English
• Leaves: 390
• Series: Developments in Mathematics 47
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
The Fundamentals of the Theory of Integrability of Differential Systems....Pages 1-33
Jacobian and Inverse Jacobian Multipliers....Pages 35-88
Darboux and Liouvillian Integrability....Pages 89-148
Existence and Degree of Darboux Polynomials....Pages 149-195
Algebraic, Analytic and Meromorphic Integrability....Pages 197-252
Applications of the Darboux Theory of Integrability....Pages 253-285
Local Integrability of Differential Systems....Pages 287-351
Back Matter....Pages 353-380

✦ Subjects

Ordinary Differential Equations;Applications of Nonlinear Dynamics and Chaos Theory