A sufficient condition for the uniqueness of normal forms and unique normal forms of generalized Hopf singularities

Jianping Peng; Duo Wang

doi:10.1142/S0218127404011247

A sufficient condition for the uniqueness of normal forms and unique normal forms of generalized Hopf singularities

Jianping Peng^*, Duo Wang

^*Corresponding author for this work

Peking University

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

A sufficient condition for the uniqueness of the Nth order normal form is provided. A new grading function is proposed and used to prove the uniqueness of the first-order normal forms of generalized Hopf singularities. Recursive formulas for computation of coefficients of unique normal forms of generalized Hopf singularities are also presented.

Original language	English
Pages (from-to)	3337-3345
Number of pages	9
Journal	International Journal of Bifurcation and Chaos
Volume	14
Issue number	9
DOIs	https://doi.org/10.1142/S0218127404011247
Publication status	Published - Sept 2004
Externally published	Yes

Keywords

Generalized Hopf singularities
Grading function
Unique normal form

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10.1142/S0218127404011247

Cite this

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title = "A sufficient condition for the uniqueness of normal forms and unique normal forms of generalized Hopf singularities",

abstract = "A sufficient condition for the uniqueness of the Nth order normal form is provided. A new grading function is proposed and used to prove the uniqueness of the first-order normal forms of generalized Hopf singularities. Recursive formulas for computation of coefficients of unique normal forms of generalized Hopf singularities are also presented.",

keywords = "Generalized Hopf singularities, Grading function, Unique normal form",

author = "Jianping Peng and Duo Wang",

note = "Funding Information: This work was supported by the Natural Science Foundation of China (No 10271007) and RFDP (No 20010001042).",

year = "2004",

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AU - Peng, Jianping

AU - Wang, Duo

N1 - Funding Information: This work was supported by the Natural Science Foundation of China (No 10271007) and RFDP (No 20010001042).

PY - 2004/9

Y1 - 2004/9

N2 - A sufficient condition for the uniqueness of the Nth order normal form is provided. A new grading function is proposed and used to prove the uniqueness of the first-order normal forms of generalized Hopf singularities. Recursive formulas for computation of coefficients of unique normal forms of generalized Hopf singularities are also presented.

AB - A sufficient condition for the uniqueness of the Nth order normal form is provided. A new grading function is proposed and used to prove the uniqueness of the first-order normal forms of generalized Hopf singularities. Recursive formulas for computation of coefficients of unique normal forms of generalized Hopf singularities are also presented.

KW - Generalized Hopf singularities

KW - Grading function

KW - Unique normal form

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DO - 10.1142/S0218127404011247

M3 - Article

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JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

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ER -

A sufficient condition for the uniqueness of normal forms and unique normal forms of generalized Hopf singularities

Abstract

Keywords

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