Linear Grading Function and Further Reduction of Normal Forms

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In this note an idea of quasi-homogeneous normal form theory using new grading functions is introduced, the definition of N th order normal form is given and some sufficient conditions for the uniqueness of normal forms are derived. A special case of the unsolved problem in a paper of Baider and Sanders for the unique normal form of Bogdanov-Takens singularities is solved.

Document Type: Research Article

Affiliations: 1: Department of Mathematics, Kyoto University, Kyoto, 606-01, Japan 2: Faculty of Science and Technology, Ryukoku University, Seta, Otsu, 520-21, Japan 3: Department of Applied Mathematics, Tsinghua University, Beijing, 100084, People's Republic of China

Publication date: December 1, 1996

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