Qualitative Theory of Dynamical Systems

, Volume 11, Issue 1, pp 111–128

Abelian Integrals and Limit Cycles


DOI: 10.1007/s12346-011-0051-z

Cite this article as:
Li, C. Qual. Theory Dyn. Syst. (2012) 11: 111. doi:10.1007/s12346-011-0051-z


This survey paper is devoted to introducing some basic concepts and methods about the application of Abelian integral to study the number of limit cycles, especially to the weak Hilbert’s 16th problem. We will introduce some recent results in this field.


Abelian integralLimit cycleWeak Hilbert’s 16th problem

Mathematics Subject Classification (2000)


Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina