Detecting alien limit cycles near a Hamiltonian 2-saddle cycle

DOI10.3934/dcds.2009.25.1081zbMath1194.34084OpenAlexW2030479805MaRDI QIDQ1045767

Robert Roussarie, Magdalena Caubergh, Freddy Dumortier, Stijn E. Luca

Publication date: 16 December 2009

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2009.25.1081

zbMATH Keywords

limit cycleAbelian integraltransition mapalien limit cycle perturbation of Hamiltonian systemPlanar vector fieldtwo-saddle cycle

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) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting ⋮ GLOBAL CLASSIFICATION OF A CLASS OF CUBIC VECTOR FIELDS WHOSE CANONICAL REGIONS ARE PERIOD ANNULI ⋮ Limit cycle bifurcations near a 2-polycycle or double 2-polycycle of planar systems ⋮ On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields ⋮ Perturbations of quadratic Hamiltonian two-saddle cycles

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