Bifurcation of limit cycles in the neighborhood of generic hyperbolic polycycles with three vertices

DOI10.5802/afst.780zbMath0805.58053OpenAlexW2327291577MaRDI QIDQ1332132

Abderaouf Mourtada

Publication date: 1 February 1995

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1994_6_3_2_259_0

zbMATH Keywords

limit cyclesbifurcation16th Hilbert problemhyperbolic polycycles

Mathematics Subject Classification ID

Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (7)

Fractal analysis of hyperbolic saddles with applications ⋮ The Fatou coordinate for parabolic Dulac germs ⋮ Tubular neighborhoods of orbits of power-logarithmic germs ⋮ Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle ⋮ Bifurcation of limit cycles near polycycles with \(n\) vertices ⋮ Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan. Algorithme de finitude. (Finite cyclicity of hyperbolic polycycles of plane vector fields. Finiteness algorithm) ⋮ Bifurcations of zeros in translated families of functions and applications

Cites Work

• Keeping track of limit cycles
• Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan. Algorithme de finitude. (Finite cyclicity of hyperbolic polycycles of plane vector fields. Finiteness algorithm)
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation
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