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

JIANPING PENG

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

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and

DUO WANG

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

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https://doi.org/10.1142/S0218127404011247Cited by:11 (Source: Crossref)

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.

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