论文信息 - A Criterion for Determining the Monotonicity of the Ratio of Two Abelian Integrals

A Criterion for Determining the Monotonicity of the Ratio of Two Abelian Integrals

Abstract A new method to determine the monotonicity of the ratio of two Abelian integrals is given. We find two criterion functions defined directly by the functions which appear in the Abelian integrals. The monotonicities of the criterion functions imply the monotonicity of the ratio of the Abelian integrals. By using this criterion, several known results can be deduced easier, and some new results are obtained.

Chengzhi Li | Zhifen Zhang

[1] R. I. Bogdanov. Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvalues , 1975 .

[2] Vladimir Igorevich Arnold,et al. Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[3] Shui-Nee Chow,et al. Abelian integrals and bifurcation theory , 1985 .

[4] Jan A. Sanders,et al. A codimension two bifurcation with a third order Picard-Fuchs equation , 1985 .

[5] Abelian integrals and global hopf bifurcations , 1985 .

[6] B. Drachman,et al. Abelian integrals for quadratic vector fields. , 1987 .

[7] S. Chow,et al. Uniqueness of periodic orbits of some vector fields with codimension two singularities , 1989 .

[8] J. Sotomayor,et al. Abelian integrals in unfoldings of codimension 3 singular planar vector fields , 1991 .

[9] H. Zoladek,et al. Quadratic Systems with Center and Their Perturbations , 1994 .