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In studying nonlinear dynamical problems, we usually restrict our analysis to the flow on the centre manifold near a equilibrium solution. The centre manifold theory of chapter 4 gives a reduction in the dimension of the system. The aim of the normal form theory is to find a nonlinear analytic transformation of coordinates to change the nonlinear system restricted to the center manifold into a “simpler” form, called normal form.

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Normal Forms

  • 章节

  • 发表日期：

    2026年

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  • Arnaud Ducrot,
  • Quentin Griette,
  • Zhihua Liu,
  • Pierre Magal

摘要

In studying nonlinear dynamical problems, we usually restrict our analysis to the flow on the centre manifold near a equilibrium solution. The centre manifold theory of chapter 4 gives a reduction in the dimension of the system. The aim of the normal form theory is to find a nonlinear analytic transformation of coordinates to change the nonlinear system restricted to the center manifold into a “simpler” form, called normal form.