Journal of Applied Analysis & Computation· 2026Q2
NEW UPPER BOUNDS ON THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR THREE PERTURBED QUADRATIC REVERSIBLE SYSTEMS
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- Q2SCImago
- 2026year
Short summary
New, improved upper bounds on the number of zeros for Abelian integrals of three specific perturbed quadratic reversible systems (r12, r16, r18) were derived using Riccati and Picard-Fuchs equations.
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Key points
- Derived new upper bounds on the number of zeros for Abelian integrals in perturbed quadratic reversible systems r12, r16, and r18.
- Utilized Riccati equation and Picard-Fuchs equation methods for the analysis.
- Considered both highest and lowest degree polynomials and their inter-term relationships.
- Obtained bounds that are demonstrably better than previously established ones.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Journal of Applied Analysis & Computation, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics