Limit cycles of resonant four-dimensional polynomial systems

作者：Llibre Jaume^*; Mereu Ana Cristina; Teixeira Marco A

来源：Dynamical Systems, 2010, 25(2): 145-158.

DOI：10.1080/14689360903348073

• limit cycle
• periodic orbit
• averaging theory
• resonance

We study the bifurcation of limit cycles from four-dimensional centres inside a class of polynomial differential systems. Our results establish an upper bound for the number of limit cycles which can be prolonged in function of the degree of the polynomial perturbation considered, up to first-order expansion of the displacement function with respect to small parameter. The main tool for proving such results is the averaging theory.

• 出版日期2010