Limit cycles bifurcating from planar polynomial quasi-homogeneous centers

DOI10.1016/j.jde.2015.08.014zbMath1332.34066OpenAlexW1841872528MaRDI QIDQ499530

Maite Grau, Jaume Llibre, Jaume Giné

Publication date: 30 September 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.08.014

zbMATH Keywords

bifurcation of limit cyclequasi-homogeneous centerquasi-homogeneous polynomial differential equation

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) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (8)

Analysis of degenerate fold-Hopf bifurcation in a three-dimensional differential system ⋮ On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center ⋮ Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems ⋮ Centers of weight-homogeneous polynomial vector fields on the plane ⋮ Center Problem for Quasi-Homogeneous Polynomial Systems with a Given Weight Degree ⋮ Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ LIMIT CYCLES FOR TWO CLASSES OF PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH UNIFORM ISOCHRONOUS CENTERS

Cites Work

• Unnamed Item
• Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems
• Cubic homogeneous polynomial centers
• Limit cycles bifurcating from the period annulus of quasi-homogeneous centers
• On the cyclicity of weight-homogeneous centers
• Averaging theory at any order for computing periodic orbits
• Planar quasi-homogeneous polynomial differential systems and their integrability

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