Small-amplitude limit cycles of Liénard systems (Q804786)

The paper is a contribution to the solution of the second part of Hilbert's sixteenth problem. The equation ẍ\(+f(x)\dot x+g(x)=0\) is transformed into \(\dot x=y-F(x)\), \(\dot y=-g(x)\); \(F(x)=\int^{x}_{0}f(\xi)d\xi\). The author calculates the maximum number of small-amplitude limit cycles, for f,g having specified orders, which may be bifurcated from the origin. Extensive computations are carried out on computer using a symbolic manipulation software package.