abelian integral
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2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Junning Cai ◽  
Minzhi Wei ◽  
Guoping Pang

In the presented paper, the Abelian integral I h of a Liénard system is investigated, with a heteroclinic loop passing through a nilpotent saddle. By using a new algebraic criterion, we try to find the least upper bound of the number of limit cycles bifurcating from periodic annulus.


2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Minzhi Wei ◽  
Junning Cai ◽  
Hongying Zhu

In present paper, the number of zeros of the Abelian integral is studied, which is for some perturbed Hamiltonian system of degree 6. We prove the generating elements of the Abelian integral from a Chebyshev system of accuracy of 3; therefore there are at most 6 zeros of the Abelian integral.


2018 ◽  
Vol 28 (05) ◽  
pp. 1850063 ◽  
Author(s):  
Shiyou Sui ◽  
Liqin Zhao

In this paper, we consider the number of zeros of Abelian integral for the system [Formula: see text], [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are arbitrary polynomials of degree [Formula: see text]. We obtain that [Formula: see text] if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] is the maximum number of limit cycles bifurcating from the period annulus up to the first order in [Formula: see text]. So, the bounds for [Formula: see text] or [Formula: see text], [Formula: see text], [Formula: see text] are exact.


2017 ◽  
Vol 27 (13) ◽  
pp. 1750196 ◽  
Author(s):  
Shiyou Sui ◽  
Baoyi Li

This paper investigates the planar differential systems [Formula: see text], [Formula: see text] under the perturbations of polynomials of [Formula: see text] with degree [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text]. The upper bound for the number of zeros of Abelian integral from the period annulus around the center is obtained.


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