Perturbations of a Hamiltonian family of cubic vector fields

DOI10.1017/S0004972700029531zbMath0747.34018OpenAlexW2045781196MaRDI QIDQ3971343

Moisés Cañas, Guillermo León de la Barra, Mario León de la Barra, Ana María Urbina

Publication date: 25 June 1992

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700029531

zbMATH Keywords

limit cyclesHamiltonianperturbationsbifurcationssaddle pointsphase portraitcubic vector fieldsHilbert's sixteenth problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Geometric methods in ordinary differential equations (34A26) Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10)

Cites Work

• Phase portraits and bifurcations of the non-linear oscillator: \(x+(\alpha+\gamma x^ 2)x'+\beta x+\delta x^ 3=0\)
• A survey of quadratic systems
• Some cubic systems with several limit cycles
• The number of limit cycles of certain polynomial differential equations
• On General Properties of Quadratic Systems

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