In this work we consider the polynomial differential system \(\dot{x} = -y + x f(y)\), \(\dot{y} =x + y f(x)\), where f is a polynomial. This system is a certain generalization of the classical Liénard system. For that system, we solve the center problem for such family and compute the order of degeneracy of a weak focus for obtaining the maximum number of small-amplitude limit cycles.

中文翻译：

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某些平面微分系统的小振幅极限环

在这项工作中，我们考虑多项式微分系统\（\ dot {x} = -y + xf（y）\），\（\ dot {y} = x + yf（x）\），其中f是多项式。该系统是经典Liénard系统的某种概括。对于该系统，我们解决了此类族群的中心问题，并计算了弱焦点的简并性顺序，以获得最大数量的小幅度极限循环。