Generalized normal forms for two-dimensional systems of ordinary differential equations with linear and quadratic unperturbed parts

DOI10.3103/S1063454107010025zbMath1152.34026OpenAlexW2024588985MaRDI QIDQ945971

B. E. Eshmatov

Publication date: 22 September 2008

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

Full work available at URL: https://doi.org/10.3103/s1063454107010025

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Normal forms for dynamical systems (37G05)

Related Items (2)

A generalized normal form and formal equivalence of two-dimensional systems with quadratic zero approximation. IV ⋮ 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

Cites Work

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• Unique normal forms for vector fields and Hamiltonians
• Linear grading function and further reduction of normal forms
• Invariant normal forms of formal series
• Further reduction of the Takens-Bogdanov normal form
• A generalized normal form and formal equivalence of systems of differential equations with zero characteristic numbers
• A generalized normal form and formal equivalence of two-dimensional systems with quadratic zero approximation. I
• A generalized normal form and formal equivalence of two-dimensional systems with quadratic zero approximation. II
• Normal forms for singularities of vector fields

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