This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping. Explicit estimates of the size of the domain on which the number of limit cycles is controlled are important in many applications of bifurcation theory (for instance in Biology and Physiology).
Detecting the limit cycles for a class of Hamiltonian systems under thirteen-order perturbed terms
On the number of limit cycles for Bogdanov-Takens system under perturbations of piecewise smooth polynomials
Chemical systems with limit cycles
![QR code for arXiv:math/0110121 [math.DS]](http://oss.arxitics.com/images/favicon.svg)