Limit Cycles of Differential Equations

  • Colin Christopher
  • Chengzhi Li

Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Around the Center-Focus Problem

    1. Front Matter
      Pages 1-3
    2. Pages 17-23
    3. Pages 33-39
    4. Pages 41-48
    5. Pages 49-54
    6. Pages 79-84
    7. Back Matter
      Pages 85-89
  3. Abelian Integrals and Applications to the Weak Hilbert’s 16th Problem

  4. Back Matter
    Pages 159-171

About this book


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 abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems.


Abelian integral Center-focus problem Differential equation Hilbert's 16th problem Limit cycle dynamical systems

Authors and affiliations

  • Colin Christopher
    • 1
  • Chengzhi Li
    • 2
  1. 1.School of Mathematics and StatisticsUniversity of PlymouthPlymouthUK
  2. 2.School of Mathematical SciencesBeijing UniversityBeijingChina

Bibliographic information