The monotonicity of the ratio of hyperelliptic integrals

DOI10.1016/j.bulsci.2014.02.001zbMath1316.34032OpenAlexW2046823797MaRDI QIDQ744070

Na Wang, Dongmei Xiao, Jiang Yu

Publication date: 6 October 2014

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2014.02.001

zbMATH Keywords

hyperbolic curveabelian integralweakened Hilbert's 16th problem

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

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The monotonicity of the ratio of two hyperelliptic abelian integrals for a class of symmetric potential systems of degree eight ⋮ Near-ordinary periodic waves of a generalized reaction-convection-diffusion equation ⋮ The monotonicity of ratios of some abelian integrals ⋮ Dynamical analysis on traveling wave of a reaction-diffusion model ⋮ On the monotonicity of the ratio of some hyperelliptic integrals of order 7

Cites Work

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• A Chebyshev criterion for Abelian integrals
• Complete hyperelliptic integrals of the first kind and their non-oscillation
• Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop
• Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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