Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7

被引：4
作者：
Bakhshalizadeh, A. [1 ]
Asheghi, R. [1 ]
Hoseyni, R. [1 ]
机构：
[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran
来源：
CHAOS SOLITONS & FRACTALS | 2017年 / 103卷
关键词：
Chebyshev's property; Hyperelliptic integrals of first kind; Hamiltonian of degree 7; Hilbert-Arnold problem;
D O I：
10.1016/j.chaos.2017.06.021
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Chebyshevs property of the three-dimensional vector space E = < J(0), J(1), J(2) >, where J(i)(h) = integral(H=h) x(i)dx/y and H(x,y)=1/2 y(2)+V(x) is a hyperelliptic Hamiltonian of degree 7. Our main result asserts that in two specific cases, namely (a) V'(x)=x(3) (x-4/7) (x-1)(2) and (b) V'(x) = x(x-2/7) (x-1)(4), E is an extended complete Chebyshev system. To this end, we use the criterion and the tools developed by GrauManosasVilladelprat in Trans. Amer. Math. Soc. in 2011. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：279 / 288
页数：10
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