Uniqueness of periodic orbits of some vector fields with codimension two singularities

DOI10.1016/0022-0396(89)90143-5zbMath0686.34040OpenAlexW2028663304MaRDI QIDQ1262439

Duo Wang, Chengzhi Li, Shui-Nee Chow

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-0396(89)90143-5

zbMATH Keywords

periodic orbituniqueness of limit cyclessmall parameters

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25)

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Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A codimension two bifurcation with a third order Picard-Fuchs equation
• Abelian integrals and bifurcation theory
• A note on: Abelian integrals and bifurcation theory
• Bifurcations of certain family of planar vector fields tangent to axes
• Singularities of vector fields
• Periodic and Steady-State Mode Interactions Lead to Tori
• ON THE VERSALITY OF A FAMILY OF SYMMETRIC VECTOR FIELDS IN THE PLANE
• Nonresonant Bifurcations with Symmetry
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