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

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.Mathematics, Interdisciplinary ApplicationsMultidisciplinary SciencesSCI(E)0ARTICLE93337-33451