
Research Article


An Improved Recursive Formula for Computing Normal Forms of Multidimensional Dynamical Systems


Lei Guo,
Qunhong Li
and
Zigen Song


ABSTRACT

In this study, an improved explicit recursive formula of normal
forms under nonlinear nearidentity transformations is firstly introduced and
the associated proof is also given out. Compared with traditional method, the
improved method can get the specific expression of the higher order terms of
dynamical systems after nonlinear transformations. So the normal forms of the
original dynamical systems can be obtained by a series of nonlinear transformations
but without changing its topology structure, also by solving a series of algebra
equations with the aid of computing software Maple, not only the coefficients
of the jth order normal form and the associated nonlinear transformations but
also higher (>j) order terms of the original equations can be obtained. The
application of the improved method will greatly simplify the computation during
the research of dynamical systems.






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