A SUFFICIENT CONDITION FOR THE UNIQUENESS OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF GENERALIZED HOPF SINGULARITIES

DOI10.1142/S0218127404011247zbMath1129.37333MaRDI QIDQ4655722

Duo Wang, Jianping Peng

Publication date: 8 March 2005

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

zbMATH Keywords

grading functionUnique normal formgeneralized Hopf singularities

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (8)

INFINITE ORDER PARAMETRIC NORMAL FORM OF HOPF SINGULARITY ⋮ Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields ⋮ FURTHER REDUCTION OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF SMOOTH MAPS ⋮ Spectral sequences and parametric normal forms ⋮ Parametric normal forms for Bogdanov-Takens singularity; the generalized saddle-node case ⋮ STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE ⋮ Unique normal form of a class of 3 dimensional vector fields with symmetries ⋮ FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS

Cites Work

• Linear grading function and further reduction of normal forms
• Smooth equivalence of germs of vector fields with a single zero eigenvalue or a pair of purely imaginary eigenvalues
• Further reduction of the Takens-Bogdanov normal form
• Computation of normal forms
• Unique normal forms for Hopf-zero vector fields.
• Unique normal form of Bogdanov-Takens singularities
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• Normal forms for singularities of vector fields
• AN EFFICIENT METHOD FOR COMPUTING THE SIMPLEST NORMAL FORMS OF VECTOR FIELDS
• Normal forms for nonlinear vector fields. I. Theory and algorithm
• UNIQUE NORMAL FORMS FOR NILPOTENT PLANAR VECTOR FIELDS
• SIMPLEST NORMAL FORMS OF HOPF AND GENERALIZED HOPF BIFURCATIONS
• Erratum to ``Poincaré renormalized forms

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