The Perturbation of a Class of Hyper-Elliptic Hamilton System with a Double Eight Figure Loop

作者：Yang, Jihua; Zhao, Liqin^*

来源：Qualitative Theory of Dynamical Systems, 2017, 16(2): 317-360.

DOI：10.1007/s12346-016-0194-z

• Hyper-elliptic
• Double eight figure loop
• Abelian integral
• Extended complete Chebyshev systems

In this paper, we consider the upper bounds of the number of isolated zeros of Abelian integrals associated to system @@@ x(over dot) = y, y(over dot) = -(x(5) - 5/2x(3) + x) @@@ under the perturbation of is an element of (alpha(0) + alpha(1)x + alpha(2)x(2) + alpha(3)x(3) + alpha(4)x(4)) y partial derivative/partial derivative y, where 0 < | is an element of | << 1 and alpha(i) is an element of R, i = 0, 1, 2, 3, 4. The unperturbed system has a double eight figure loop. The sharp upper bounds are obtained for ten cases that two of five parameters vanish.

• 出版日期2017-7
• 单位北京师范大学; 宁夏师范学院