Unfolding of the Hamiltonian triangle vector field

DOI10.1007/s10883-011-9120-5zbMath1228.34057OpenAlexW2045828312MaRDI QIDQ548717

Yong-Cai Geng, Sumit K. Garg

Publication date: 30 June 2011

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/128141

zbMATH Keywords

limit cyclesdisplacement functionabelian integrals

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45)

Related Items (7)

Some integral inequalities for coordinated log-\(h\)-convex interval-valued functions ⋮ Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle ⋮ The maximal number of limit cycles bifurcating from a Hamiltonian triangle in quadratic systems ⋮ Principal part of multi-parameter displacement functions ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs ⋮ Melnikov functions in quadratic perturbations of generalized Lotka-Volterra systems ⋮ Essential perturbations of polynomial vector fields with a period annulus

Cites Work

• Higher order Poincaré-Pontryagin functions and iterated path integrals
• Perturbations of symmetric elliptic Hamiltonians of degree four
• Principal Poincaré-Pontryagin function of polynomial perturbations of the Hamiltonian triangle
• Bifurcations of certain family of planar vector fields tangent to axes
• Quadratic systems with center and their perturbations
• Perturbations of quadratic centers
• On cyclicity of triangles and segments in quadratic systems
• Higher-order Melnikov functions for degenerate cubic Hamiltonians
• The cyclicity of the period annulus of the quadratic Hamiltonian triangle
• The displacement map associated to polynominal unfoldings of planar Hamiltonian vector fields

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