On the monotonicity of the ratio of some hyperelliptic integrals of order 7

DOI10.1016/j.bulsci.2019.102810zbMath1434.34032OpenAlexW2987463925WikidataQ126845646 ScholiaQ126845646MaRDI QIDQ2287837

A. Bakhshalizadeh, Rasool Kazemi, Rasoul Asheghi

Publication date: 21 January 2020

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

Full work available at URL: https://doi.org/10.1016/j.bulsci.2019.102810

zbMATH Keywords

monotonicityHamiltonian functionhyperelliptic integralsalgebraic criteria

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (1)

The monotonicity of the ratio of two hyperelliptic abelian integrals for a class of symmetric potential systems of degree eight

Cites Work

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• Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system
• The monotonicity of the ratio of hyperelliptic integrals
• Limit cycles of differential equations
• Limit cycles near homoclinic and heteroclinic loops
• A criterion for determining the monotonicity of the ratio of two Abelian integrals
• The monotonicity of the ratio of two Abelian integrals
• A Chebyshev criterion for Abelian integrals

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