Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves-Reference-Cited by-同舟云学术

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

Published:2016-02 Issue:02 Volume:26 Page:1650020
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Hong Xiaochun¹,Xie Shaolong²,Chen Longwei³

Affiliation:

1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan TongChuang Scientific Computing and Data Mining Research Center, Kunming, Yunnan 650221, P. R. China

2. Business School, Yuxi Normal University, Yuxi, Yunnan 653100, P. R. China

3. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, P. R. China

Abstract

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].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127416500206

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