Qualitative Theory of Planar Differential Systems

• Main Authors: Dumortier, Freddy (Author), Llibre, Jaume (Author), Artés, Joan C. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Ordinary Differential Equations.; Dynamical Systems and Ergodic Theory.

The book deals essentially with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability....

Table of Contents:

• Basic Results on the Qualitative Theory of Differential Equations
• Normal Forms and Elementary Singularities
• Desingularization of Nonelementary Singularities
• Centers and Lyapunov Constants
• Poincaré and Poincaré–Lyapunov Compactification
• Indices of Planar Singular Points
• Limit Cycles and Structural Stability
• Integrability and Algebraic Solutions in Polynomial Vector Fields
• Polynomial Planar Phase Portraits
• Examples for Running P4.