Details:
Title  Higher order limit cycle bifurcations from nondegenerate centers  Author(s)  Jaume Giné  Type  Article in Journal  Abstract  The computational problems which appear in the computation of the Poincaré–Liapunov constants and the determination of their functionally independent number has led in recent works to consider only the lowest terms of these constants. In this work we improve the results obtained in this direction for polynomials systems of the form x ˙ =  y + P n ( x , y ) , y ˙ = x + Q n ( x , y ) , where P n and Q n are a homogeneous polynomial of degree n. We use center bifurcation to estimate the cyclicity of a unique singular point of focuscenter type for different values of n and compare with the results given by the conjecture presented in [15].  Keywords  Poincaré–Liapunov constants, Limit cycles, Center problem, Groebner basis  ISSN  00963003 
URL 
http://www.sciencedirect.com/science/article/pii/S0096300312001713 
Language  English  Journal  Applied Mathematics and Computation  Volume  218  Number  17  Pages  8853  8860  Year  2012  Edition  0  Translation 
No  Refereed 
No 
