Limit Cycles of Differential Equations

• Main Authors: Christopher, Colin (Author), Li, Chengzhi (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2007.
• Series: Advanced Courses in Mathematics CRM Barcelona
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Ordinary Differential Equations.; Dynamical Systems and Ergodic Theory.

This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006. The topics covered are the center-focus problem for polynomial vector fields, and the application of abel...

Table of Contents:

• Around the Center-Focus Problem
• Centers and Limit Cycles
• Darboux Integrability
• Liouvillian Integrability
• Symmetry
• Cherkas’ Systems
• Monodromy
• The Tangential Center-Focus Problem
• Monodromy of Hyperelliptic Abelian Integrals
• Holonomy and the Lotka-Volterra System
• Other Approaches
• Abelian Integrals and Applications to the Weak Hilbert’s 16th Problem
• Hilbert’s 16th Problem and Its Weak Form
• Abelian Integrals and Limit Cycles
• Estimate of the Number of Zeros of Abelian Integrals
• A Unified Proof of the Weak Hilbert’s 16th Problem for n=2.