Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7

DOI10.1016/j.chaos.2017.06.021zbMath1375.34048OpenAlexW2718616714WikidataQ114199232 ScholiaQ114199232MaRDI QIDQ1681678

A. Bakhshalizadeh, R. Hoseyni, Rasoul Asheghi

Publication date: 24 November 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2017.06.021

zbMATH Keywords

Hilbert-Arnold problemChebyshev's propertyHamiltonian of degree 7hyperelliptic integrals of first kind

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)

Related Items (3)

Limit cycle bifurcations for a kind of Liénard system with degree seven ⋮ The dynamics of a kind of Liénard system with sixth degree and its limit cycle bifurcations under perturbations ⋮ ON THE NUMBER OF LIMIT CYCLES FOR A QUINTIC LIÉNARD SYSTEM UNDER POLYNOMIAL PERTURBATIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Chebyshev's property of certain hyperelliptic integrals of the first kind
• Bounding the number of zeros of certain abelian integrals
• The exact bounds on the number of zeros of complete hyperelliptic integrals of the first kind
• Chebyshev property of complete elliptic integrals and its application to Abelian integrals.
• Elliptic integrals and their nonoscillation
• Abelian integrals related to Morse polynomials and perturbations of plane Hamiltonian vector fields
• A Chebyshev criterion for Abelian integrals
• Complete hyperelliptic integrals of the first kind and their non-oscillation

This page was built for publication: Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7