Work

New Upper Bounds on the Number of Zeros of Abelian Integrals for Three Perturbed Quadratic Reversible Systems

Year: 2026

Type: article

Abstract: For the quadratic reversible systems $r12$, $r16$ and $r18$, when they are perturbed by arbitrary polynomial of degree $n$, we explore the new upper bounds on the number of zeros for their Abelian integrals using the methods of Riccati equation and Picard-Fuchs equation. We consider both the highest degree and the lowest degree of the related polynomials, and more importantly, we notice their law between the terms, and take into account the range of values for variable. Some laws of related polynomials of the systems have been found, therefore, we obtain some new upper bounds, which are better than those obtained before.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20260150

Authors: Xiaochun Hong, Jing Chang, Lijun Hong, Ronghua Cheng, Wei Lu

Institutions: Zhuhai College of Science and Technology, Sun Yat-sen University, Yunnan University of Finance And Economics

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation, Yunnan University of Finance and Economics

OpenAlex ID: W7222726253