摘要：In this article, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of seventh-degree systems are investigated. With the help of computer algebra system MATHEMATICA, the first 13 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The result that there exist 13 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth, we give a lower bound of cyclicity of three-order nilpotent critical point for seventh-degree nilpotent systems. MSC: 34C05; 34C07.
关键词：three-order nilpotent critical point ; center-focus problem ; bifurcation of limit cycles ; quasi-Lyapunov constant
