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- Title
Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One.
- Authors
Qiuli Yu; Houmei He; Yuangen Zhan; Xiaochun Hong
- Abstract
By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree n. We obtain that the upper bound is 7[(n - 3)/2] + 5 when n = 5, 8 when n = 4, 5 when n = 3, 4 when n = 2, and 0 when n = 1 or n = 0, which linearly depends on n.
- Subjects
RICCATI equation; DIFFERENTIAL equations; POLYNOMIALS; DYNAMICAL systems; ALGEBRAIC geometry
- Publication
Journal of Nonlinear Modeling & Analysis, 2024, Vol 6, Issue 1, p218
- ISSN
2562-2854
- Publication type
Article
- DOI
10.12150/jnma.2024.218