Global Phase Portraits of ℤ2-Symmetric Planar Polynomial Hamiltonian Systems of Degree Three with a Nilpotent Saddle at the Origin

DOI10.1142/S0218127420500066zbMath1436.34025OpenAlexW3006289102MaRDI QIDQ5220439

Montserrat Corbera, Claudia Valls

Publication date: 23 March 2020

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127420500066

zbMATH Keywords

phase portraitnilpotent saddlepolynomial Hamiltonian systemsPoincaré compactification

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Cites Work

• \(Z_{2}\)-equivariant cubic system which yields 13 limit cycles
• Global bifurcations in a perturbed cubic system with \(Z_ 2\)-symmetry
• On polynomial Hamiltonian planar vector fields
• Polynomial Hamiltonian systems of degree 3 with symmetric nilpotent centers
• Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
• On limit cycles of the Liénard equation with \(Z_2\) symmetry
• Qualitative theory of planar differential systems
• A SURVEY ON THE BLOW UP TECHNIQUE
• Global Phase Portraits for the Abel Quadratic Polynomial Differential Equations of the Second Kind With Z₂-symmetries

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