scholarly journals UPPER BOUNDS FOR THE ASSOCIATED NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR TWO CLASSES OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE

2018 ◽  
Vol 8 (6) ◽  
pp. 1959-1970 ◽  
Author(s):  
Xiaochun Hong ◽  
◽  
Junliang Lu ◽  
Yanjie Wang
Keyword(s):  
Upper Bounds ◽  
Abelian Integrals ◽  
Number Of Zeros ◽  
Genus One

Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves

2016 ◽  
Vol 26 (02) ◽  
pp. 1650020 ◽  
Author(s):  
Xiaochun Hong ◽  
Shaolong Xie ◽  
Longwei Chen
Keyword(s):  
Upper Bounds ◽  
Higher Order ◽  
Abelian Integrals ◽  
Arbitrary Degree ◽  
Number Of Zeros ◽  
Genus One

In this study, we determine the associated number of zeros for Abelian integrals in four classes of quadratic reversible centers of genus one. Based on the results of [Li et al., 2002b],, we prove that the upper bounds of the associated number of zeros for Abelian integrals with orbits formed by conics, cubics, quartics, and sextics, under polynomial perturbations of arbitrary degree [Formula: see text], depend linearly on [Formula: see text].

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

scholarly journals ON THE NUMBER OF ZEROS OF THE ABELIAN INTEGRALS FOR A CLASS OF PERTURBED LIÉNARD SYSTEMS

2007 ◽  
Vol 17 (09) ◽  
pp. 3281-3287
Author(s):  
TONGHUA ZHANG ◽  
YU-CHU TIAN ◽  
MOSES O. TADÉ
Keyword(s):  
Algebraic Structure ◽  
Upper Bound ◽  
Abelian Integrals ◽  
Hilbert’S 16Th Problem ◽  
Number Of Zeros ◽  
Liénard Systems ◽  
Hilbert's 16Th Problem

Addressing the weakened Hilbert's 16th problem or the Hilbert–Arnold problem, this paper gives an upper bound B(n) ≤ 7n + 5 for the number of zeros of the Abelian integrals for a class of Liénard systems. We proved the main result using the Picard–Fuchs equations and the algebraic structure of the integrals.

scholarly journals Upper bounds for the number of zeroes for some Abelian integrals

2012 ◽  
Vol 75 (13) ◽  
pp. 5169-5179 ◽  
Author(s):  
Armengol Gasull ◽  
J. Tomás Lázaro ◽  
Joan Torregrosa
Keyword(s):  
Upper Bounds ◽  
Abelian Integrals

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
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