An Improved Version of Poincaré-Dulac Theorem for Improved Nilpotent Normal Forms
نویسندگان
چکیده
An improved version of the well-known Poincaré-Dulac’s normal form theorem is first proposed. It is shown that, for a nonlinear vector field, a normal form near a singular point can always be chosen so that the number of nonlinear components is at most equal to the number of Jordan blocks in the normalized leading matrix, thus leading to the “simplest” form in which a formal vector field can be written near a singular point. Within this scope, a generalization to any dimension of an important result on normal forms of nilpotent systems is given. This is the main result of the paper. Mathematics Subject Classification: 34C20
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