Linear estimate of the number of zeros of Abelian integrals for a class of integrable non-Hamiltonian systems

2001 ◽  
Vol 47 (7) ◽  
pp. 4527-4531 ◽  
Author(s):  
Chengzhi Li ◽  
Weigu Li ◽  
J. Llibre ◽  
Zhifen Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Abelian Integrals ◽  
Linear Estimate ◽  
Number Of Zeros

scholarly journals An explicit linear estimate for the number of zeros of Abelian integrals

Nonlinearity ◽  
2012 ◽  
Vol 25 (6) ◽  
pp. 1931-1946 ◽  
Author(s):  
Gal Binyamini ◽  
Gal Dor
Keyword(s):  
Abelian Integrals ◽  
Linear Estimate ◽  
Number Of Zeros

Linear estimate for the number of zeros of Abelian integrals for quadratic isochronous centres

Nonlinearity ◽  
2000 ◽  
Vol 13 (5) ◽  
pp. 1775-1800 ◽  
Author(s):  
Chengzhi Li ◽  
Weigu Li ◽  
Jaume Llibre ◽  
Zhifen Zhang
Keyword(s):  
Abelian Integrals ◽  
Linear Estimate ◽  
Number Of Zeros

QUADRATIC PERTURBATIONS OF A CLASS OF QUADRATIC REVERSIBLE LOTKA–VOLTERRA SYSTEMS

2013 ◽  
Vol 23 (08) ◽  
pp. 1350137
Author(s):  
YI SHAO ◽  
A. CHUNXIANG
Keyword(s):  
Limit Cycles ◽  
Positive Answer ◽  
Abelian Integrals ◽  
Volterra System ◽  
Bifurcation Of Limit Cycles ◽  
Number Of Zeros ◽  
Period Annulus ◽  
Volterra Systems

This paper is concerned with the bifurcation of limit cycles of a class of quadratic reversible Lotka–Volterra system [Formula: see text] with b = -1/3. By using the Chebyshev criterion to study the number of zeros of Abelian integrals, we prove that this system has at most two limit cycles produced from the period annulus around the center under quadratic perturbations, which provide a positive answer for a case of the conjecture proposed by S. Gautier et al.

On the number of zeros of Abelian integrals for a kind of quartic Hamiltonians

2014 ◽  
Vol 228 ◽  
pp. 329-335 ◽  
Author(s):  
Juanjuan Wu ◽  
Yongkang Zhang ◽  
Cuiping Li
Keyword(s):  
Abelian Integrals ◽  
Number Of Zeros

scholarly journals On the number of zeros of Abelian integrals

2010 ◽  
Vol 181 (2) ◽  
pp. 227-289 ◽  
Author(s):  
Gal Binyamini ◽  
Dmitry Novikov ◽  
Sergei Yakovenko
Keyword(s):  
Abelian Integrals ◽  
Number Of Zeros
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