The smallest upper bound on the number of zeros of Abelian integrals
The smallest upper bound on the number of zeros of Abelian integrals
复制标题
阿贝尔积分的零个数的最小上限
DOI：
10.1016/j.jde.2020.03.016
复制
发表时间：
2020-08
影响因子：
2.4
通讯作者：
Xiao Dongmei
中科院分区：
文献类型：
--
作者：
Liu Changjian;Xiao Dongmei
In this paper, we develop a new method to estimate the smallest upper bound on the number of isolated zeros of Abelian integrals, and give an algebraic criterion for the case of Abelian integrals along energy level ovals of potential systems. As applications of our main result, we first obtain a criterion guaranteeing that two Abelian integrals have the Chebyshev property with accuracy one and give an example of hyperelliptic Abelian integrals. Then we get a criterion that any nontrivial linear combination of three Abelian integrals has at most two isolated zeros. Using this criterion we prove that the smallest upper bound is two for the number of isolated zeros of a non-algebraic Abelian integral along the oval (y 2+ 1 2) 1 x 2+ ln| x|− 1 2= h with 0< h<+∞, which corresponds to the perturbation of a quadratic reversible system with two centers. Moreover, we derive all possible configurations of limit cycles from the Poincaré bifurcation of this perturbation. To our knowledge, these problems can not be solved by other known approaches.
登录
查看更多内容
影响因子：
0.9
作者：
H. Zoladek
通讯作者：
H. Zoladek
一类具有幂零鞍点的超椭圆哈密顿系统小扰动的极限环数
DOI：
10.1016/j.jde.2010.11.004
发表时间：
2011-02
期刊：
J. Differential Equations
影响因子：
--
作者：
Jihua Wang;Dongmei Xiao
通讯作者：
Dongmei Xiao
影响因子：
1.3
作者：
Liu Changjian;Chen Guoting;Sun Zhongqin
通讯作者：
Sun Zhongqin
影响因子：
2.4
作者：
Na Wang;Jihua Wang;Dongmei Xiao
通讯作者：
Na Wang;Jihua Wang;Dongmei Xiao
DOI：
--
发表时间：
2009
期刊：
--
影响因子：
--
作者：
Mathieu Gentes
通讯作者：
Mathieu Gentes