The monotonicity of the ratio of two hyperelliptic Abelian integrals for a class of symmetric potential systems of degree eight

被引：0
|
作者：
Mohammad, G. [1 ]
Asheghi, R. [1 ]
Kazemi, R. [2 ]
机构：
[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 84156, Iran
[2] Univ Kashan, Dept Math Sci, Kashan 87317, Iran
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2022年 / 176卷
关键词：
Hamiltonian systems; Hyperelliptic Abelian integrals; Monotonicity; Asymptotic expansions; CRITERION;
D O I：
10.1016/j.bulsci.2022.103130
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies the monotonicity of the ratio of two hyperelliptic Abelian integrals I-0(h) = integral & UGamma;(h) ydx and I-1(h) = integral & UGamma;(h) xydx, where & UGamma;(h) is a compact component of the level set {(x, y) & ISIN; R-2 : H(x, y) = h, h & ISIN; (h(1), h(2))}, with H(x, y) = y(2) + A(x), where A(x) is an even polynomial of degree 8 depending on two parameters alpha and beta.& nbsp;(c) 2022 Elsevier Masson SAS. All rights reserved.
引用
收藏
页数：34
相关论文
共 44 条
  • [1] MONOTONICITY OF THE RATIO OF TWO ABELIAN INTEGRALS FOR A CLASS OF SYMMETRIC HYPERELLIPTIC HAMILTONIAN SYSTEMS
    Kazemi, Rasool
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (01): : 344 - 355
  • [2] THE MONOTONICITY OF THE RATIO OF TWO ABELIAN INTEGRALS
    Liu, Changjian
    Xiao, Dongmei
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (10) : 5525 - 5544
  • [3] The monotonicity of the ratio of hyperelliptic integrals
    Wang, Na
    Xiao, Dongmei
    Yu, Jiang
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2014, 138 (07): : 805 - 845
  • [4] Criterion for determining the monotonicity of the ratio of two Abelian integrals
    Li, CZ
    Zhang, ZF
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 124 (02) : 407 - 424
  • [5] New criteria for the monotonicity of the ratio of two Abelian integrals
    Liu, Changjian
    Chen, Guoting
    Sun, Zhongqin
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 465 (01) : 220 - 234
  • [6] On the monotonicity of the ratio of some hyperelliptic integrals of order 7
    Bakhshalizadeh, A.
    Asheghi, R.
    Kazemi, R.
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2020, 158
  • [7] On the Chebyshev Property of a Class of Hyperelliptic Abelian Integrals
    Sun, Yangjian
    Wang, Shaoqing
    Yang, Jiazhong
    [J]. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (SUPPL 1)
  • [8] MONOTONICITY OF THE RATIOS OF TWO ABELIAN INTEGRALS FOR HAMILTONIAN SYSTEMS WITH PARAMETERS
    Wang, Qiaoyun
    Wang, Na
    Sun, Xianbo
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (05): : 2466 - 2487
  • [9] The Monotonicity of the Ratio of Two Line Integrals in Piecewise Smooth Differential Systems
    Bakhshalizadeh, Ali
    Asheghi, Rasoul
    [J]. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2024, 32 (03) : 785 - 798
  • [10] The monotonicity and convexity of the period function for a class of symmetric Newtonian systems of degree 8
    Kazemi, Rasool
    Akrami, Mohammad Hossein
    [J]. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2022, 10 (01): : 236 - 258
12345