Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields

DOI10.1016/j.nonrwa.2021.103451zbMath1490.34029OpenAlexW3212847365MaRDI QIDQ2061617

Claudia Valls, Montserrat Corbera

Publication date: 15 December 2021

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2021.103451

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) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (1)

Four limit cycles of discontinuous piecewise differential systems with nilpotent saddles separated by a straight line

Cites Work

• Quadratic systems with an integrable saddle: a complete classification in the coefficient space \(\mathbb R^{12}\)
• Bifurcation diagrams for Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
• Saddle quantities and applications
• Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
• Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Qualitative theory of planar differential systems
• A SURVEY ON THE BLOW UP TECHNIQUE

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