Centers of quasi-homogeneous polynomial planar systems

DOI10.1016/j.nonrwa.2011.07.056zbMath1238.34052OpenAlexW2058922238MaRDI QIDQ420064

Antonio Algaba, Cristóbal García, Natalia Fuentes

Publication date: 20 May 2012

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2011.07.056

zbMATH Keywords

integrabilitymonodromyreversibilitycenter problemquasi-homogeneous

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Smooth dynamical systems: general theory (37C99)

Related Items (28)

Analytic integrability of some examples of degenerate planar vector fields ⋮ Classification and counting of planar quasi-homogeneous differential systems through their weight vectors ⋮ Analytic integrability inside a family of degenerate centers ⋮ The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields ⋮ On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center ⋮ Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems ⋮ On the formal integrability problem for planar differential systems ⋮ On the center criterion of planar quasi-homogeneous polynomial differential systems ⋮ Comment on: ``Centers of quasi-homogeneous polynomial planar systems ⋮ Structural stability of planar quasi-homogeneous vector fields ⋮ The center problem. A view from the normal form theory ⋮ The Poincaré map of degenerate monodromic singularities with Puiseux inverse integrating factor ⋮ Classification of global phase portrait of planar quintic quasi-homogeneous coprime polynomial systems ⋮ Centers of weight-homogeneous polynomial vector fields on the plane ⋮ Analytic integrability for some degenerate planar vector fields ⋮ Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems ⋮ Center of planar quintic quasi-homogeneous polynomial differential systems ⋮ Center problem for generic degenerate vector fields ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ A note on analytic integrability of planar vector fields ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ Global dynamics of planar quasi-homogeneous differential systems ⋮ Geometric criterium in the center problem ⋮ On orbital-reversibility for a class of planar dynamical systems ⋮ A new normal form for monodromic nilpotent singularities of planar vector fields ⋮ Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems ⋮ Orbitally universal centers ⋮ Center problem with characteristic directions and inverse integrating factors

Cites Work

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• The center problem for a family of systems of differential equations having a nilpotent singular point
• On some open problems in planar differential systems and Hilbert's 16th problem
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• Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems
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