Algebraic classification of homogeneous polynomial vector fields in the plane

DOI10.1007/BF03167299zbMath0855.34031MaRDI QIDQ1922266

C. B. Collins

Publication date: 15 September 1996

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

classificationlinear equivalencetensor and spinor algebratwo-dimensional homogeneous polynomial vector fields of arbitrary degree

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Differential algebra (12H05)

Related Items

Classification and counting of planar quasi-homogeneous differential systems through their weight vectors, Phase portraits of planar semi-homogeneous vector fields. III, Global dynamics of a class of planar semi-homogeneous polynomial vector fields with degree \(2-3\), Phase portraits of planar semi-homogeneous vector fields-I, Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems, Poincaré's reversibility condition, Planar semi-quasi homogeneous polynomial differential systems with a given degree, Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems, Near-idempotents, near-nilpotents and stability of critical points for Riccati equations, On a generalization of some instability results for Riccati equations via nonassociative algebras, Algebraic and topological classification of homogeneous quartic vector fields in the plane

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