Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields

DOI10.1142/S0218127417501310zbMath1377.34049MaRDI QIDQ4599792

Duo Wang, Liying Kou, Jing Li

Publication date: 5 January 2018

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

first integralunique normal formlinear grading functionmultiple Lie bracketsthree-dimensional nilpotent vector field

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (3)

Normal forms of double Hopf oscillators with radial nonlinearities ⋮ The infinite level normal forms for non-resonant double Hopf singularities ⋮ Unique Normal Form and the Associated Coefficients for a Class of Three-Dimensional Nilpotent Vector Fields

Cites Work

• Linear grading function and further reduction of normal forms
• Unique normal forms: The nilpotent Hamiltonian case
• Hypernormal form calculation for triple-zero degeneracies
• Further reduction of the Takens-Bogdanov normal form
• Unique normal forms for Hopf-zero vector fields.
• Unique normal form of Bogdanov-Takens singularities
• Normal forms for Hopf-zero singularities with nonconservative nonlinear part
• Unique normal form of a class of 3 dimensional vector fields with symmetries
• Unique orbital normal forms for vector fields of Hopf-zero singularity
• Reduced Forms of a Singular Vector Field in <b><i>C</i></b>³ with Nilpotent Linear Part
• Normal forms for singularities of vector fields
• A SUFFICIENT CONDITION FOR THE UNIQUENESS OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF GENERALIZED HOPF SINGULARITIES
• UNIQUE NORMAL FORMS FOR NILPOTENT PLANAR VECTOR FIELDS
• A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING
• Normal forms of Hopf-zero singularity

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