LIMIT CYCLE BIFURCATIONS FROM CENTERS OF SYMMETRIC HAMILTONIAN SYSTEMS PERTURBED BY CUBIC POLYNOMIALS

DOI10.1142/S0218127413500430zbMath1270.34083arXiv1201.2709OpenAlexW3105523210MaRDI QIDQ2845167

Valery G. Romanovski, Zhaoping Hu, Bin Gao

Publication date: 22 August 2013

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

Full work available at URL: https://arxiv.org/abs/1201.2709

zbMATH Keywords

perturbationbifurcationcenterlimit cyclenear-Hamiltonian system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (3)

Classification of global phase portraits and bifurcation diagrams of Hamiltonian systems with rational potential ⋮ Limit Cycle Bifurcations from an Order-3 Nilpotent Center of Cubic Hamiltonian Systems Perturbed by Cubic Polynomials ⋮ Limit cycle bifurcations by perturbing a compound loop with a cusp and a nilpotent saddle

Cites Work

• On Hopf cyclicity of planar systems
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• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

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