Zeroes of complete elliptic integrals for 1:2 resonance

DOI10.1016/0022-0396(91)90101-EzbMath0738.33014OpenAlexW2093979069MaRDI QIDQ1181693

Henryk Żołądek, Christiane Rousseau

Publication date: 27 June 1992

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(91)90101-e

zbMATH Keywords

resonanceChebychev systemzeroes of elliptic integrals

Mathematics Subject Classification ID

Elliptic functions and integrals (33E05)

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Cites Work

• Unnamed Item
• Zeros of special abelian integrals in a real domain
• Number of zeros of complete elliptic integrals
• Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
• The Chebyshev property of elliptic integrals
• Elliptic integrals and their nonoscillation
• Abelian integrals in non-symmetric perturbation of symmetric Hamiltonian vector field
• Saddle quantities and applications
• Codimension 2 Symmetric Homoclinic Bifurcations and Application to 1:2 Resonance
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation
• Complex zeros of an elliptic integral
• Complex zeros of an elliptic integral