Unique normal form of Bogdanov-Takens singularities

DOI10.1006/jdeq.1999.3739zbMath0957.34041OpenAlexW2004439991MaRDI QIDQ1566840

Young Jiang, Jing Li, Duo Wang, Min-Hai Huang

Publication date: 28 September 2000

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

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3739

zbMATH Keywords

uniquenessordinary differential equationsnormal forms

Mathematics Subject Classification ID

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

Related Items (25)

Normal form of Bogdanov-Takens: styles and a hypernormalization method ⋮ INFINITE ORDER PARAMETRIC NORMAL FORM OF HOPF SINGULARITY ⋮ Normal forms of double Hopf oscillators with radial nonlinearities ⋮ Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields ⋮ A matching pursuit technique for computing the simplest normal forms of vector fields ⋮ The infinite level normal forms for non-resonant double Hopf singularities ⋮ BIFURCATION OF MULTIPLE LIMIT CYCLES FOR A ROTOR-ACTIVE MAGNETIC BEARINGS SYSTEM WITH TIME-VARYING STIFFNESS ⋮ FURTHER REDUCTION OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF SMOOTH MAPS ⋮ Spectral sequences and parametric normal forms ⋮ Computing simplest normal forms for the Takens-Bogdanov singularity ⋮ Parametric normal forms for Bogdanov-Takens singularity; the generalized saddle-node case ⋮ Vector potential normal form classification for completely integrable solenoidal nilpotent singularities ⋮ Normal forms of vector fields with perturbation parameters and their application ⋮ The simplest normal form and its application to bifurcation control ⋮ Unique normal form of a class of 3 dimensional vector fields with symmetries ⋮ AN EFFICIENT METHOD FOR COMPUTING THE SIMPLEST NORMAL FORMS OF VECTOR FIELDS ⋮ A SUFFICIENT CONDITION FOR THE UNIQUENESS OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF GENERALIZED HOPF SINGULARITIES ⋮ FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS ⋮ COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE ⋮ SIMPLEST NORMAL FORMS FOR PLANAR SYSTEMS ON EQUILIBRIUM MANIFOLDS ⋮ Limit cycles and homoclinic orbits and their bifurcation of Bogdanov-Takens system ⋮ UNIQUE NORMAL FORMS FOR NILPOTENT PLANAR VECTOR FIELDS ⋮ Unique orbital normal forms for vector fields of Hopf-zero singularity ⋮ Quasi-homogeneous normal forms ⋮ Computation of the simplest normal forms with perturbation parameters based on Lie transform and rescaling

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unique normal forms for vector fields and Hamiltonians
• Unique normal forms for planar vector fields
• Linear grading function and further reduction of normal forms
• Unique normal forms: The nilpotent Hamiltonian case
• Further reduction of the Takens-Bogdanov normal form
• Normal forms for singularities of vector fields
• Uniqueness and non-uniqueness of normal forms for vector fields

This page was built for publication: Unique normal form of Bogdanov-Takens singularities