Jacobi椭圆函数有理式的Fourier级数*

本文列出了手册[1]及文献[2]中未计算过的九十余个Jacobi椭圆函数sn(u,k),cn(u,k),dn(u,k)的有理函数的Fourier展式.对于用Melnikov方法研究可积系统在周期扰动下的次谐波分枝与浑沌性质,及其他工程物理中的计算问题,这些公式可供查阅应用.     

Fourier series of rational fractions of Jacobian elliptic functions

In this paper more than ninety of the Fourier series of rational fractions of Jacobian elliptic functions sn(u.k.), cn(u.k) and dn(u.k) are listed, which cannot be found in the handbook^[1] and Ref. [2]. For the detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamiltonian system subject to external periodic forcing by Melnikov's method, and for study of some problems of physical science and engineering. these formulas can be used. Proiect Supported by the Science Fund of the Chinese Academy of Sciences.     

FOURIER SERIES OF RATIONAL FRACTIONS OF JACOBIAN ELLIPTIC FUNCTIONS

In this paper more than ninety of the Fourier series of rational fractions of Jacobian elliptic fumctions sn(u,k), cn(u,k) and dn(u,k) are listed, which cannot be found in the handbood and Ref. [2]. For tile detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamihonian system subject to external periodic forcing by Melnikov's method, and for studr of some problems of physical science and engineering, these formulas can be used.     

GLOBAL BIFURCATIONS IN A DISTURBED HAMILTONIAN VECTOR FIELD APPROACHING A 3:1 RESONANT POINCAR MAP (Ⅰ)

In this paper, we use a qualitative method to study global and local bifurcations in a disturbedHamiltonian vector field approaching a Poincare map in the 3:1 resonant case. We give explicitcalculation formulas to determine bifurcation parameters and draw various bifurcations and phaseportraits in the phase plane.