具有不变直线的可积非Hamilton系统的极限环分支

Bifurcation of Limit Cycles for Integrable Non-Hamilton System with Invariant Straight Lines

研究如下扰动可积非Hamilton系统x=-y(ax^2+1)+εf(x,y),y=x(ax^2+1)+εg(x,y),其中,a<0,0<︱ε︱<<1,f(x,y)和g(x,y)是关于x、y的n次多项式.应用平均法得到该系统至少存在[n-1/2]+[n+1/2]个极限环.

This paper investigates the following perturbed integrable differential system x =-y（ ax^2＋ 1） ＋ εf（ x,y）, y = x（ ax^2＋ 1） ＋ εg（ x,y）, where a 0,0 ︱ε ︱1,f（ x,y） and g（ x,y） are polynomials in x and y of degree n. By using the averaging method,we obtain that this system has at least [n-1/2]＋[n＋1/2] limit cycles.