Number of invariant straight lines for homogeneous polynomial vector fields of arbitrary degree and dimension

DOI10.1007/s10884-009-9141-xzbMath1183.34062OpenAlexW2062732613MaRDI QIDQ735060

Violetta Pilyugina, Jaume Llibre

Publication date: 14 October 2009

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

Full work available at URL: https://doi.org/10.1007/s10884-009-9141-x

zbMATH Keywords

polynomial vector fieldinvariant straight linehomogeneous polynomial vector fieldinfinite singular point

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Invariant manifolds for ordinary differential equations (34C45)

Related Items (2)

Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in \(\mathbb R^3\) ⋮ On the number of characteristic lines for homogeneous vector fields

Cites Work

• Algebraic and topological classification of the homogeneous cubic vector fields in the plane
• Bounded Polynomial Vector Fields

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