Generalized normal forms of the systems of ordinary differential equations with a quasi-homogeneous polynomial \(( \alpha x_1^2 + x_2, x_1x_2)\) in the unperturbed part

DOI10.1134/S1063454121010040zbMath1478.34047OpenAlexW3136199172MaRDI QIDQ2038510

Yanyan Li

Publication date: 7 July 2021

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1063454121010040

zbMATH Keywords

quasi-homogeneous polynomialgeneralized normal formresonance equation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Cites Work

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• Linear grading function and further reduction of normal forms
• Generalized normal forms for two-dimensional systems of ordinary differential equations with linear and quadratic unperturbed parts
• Versal deformation of a singular point of a vector field on the plane in the case of zero eigenvalues
• Further reduction of the Takens-Bogdanov normal form
• A generalized normal form and formal equivalence of two-dimensional systems with quadratic zero approximation. I
• Singularities of vector fields

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