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Linear grading function and further reduction of normal forms. (English) Zbl 0876.34040
The concept of linear grading functions is introduced and a method to define new grading functions is given.
A quasi-homogeneous normal form theory is developed by using grading functions and \(n\)th order normal forms are defined.
The authors combine methods of Ushiki and of Baider-Sander. A special case of the unsolved problem in a paper of Baider and Sander for the unique normal form of Bogdanov-Takens is solved.

34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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