Further reduction of the Takens-Bogdanov normal form.

*(English)*Zbl 0761.34027Normal forms (analytic or formal) play an important role in the theory of systems of ODE, solving birfurcation or stability type problems. The idea of normalisation is the elimination of as many as possible terms. The authors formulate and prove a unique formal classification of analytic vector fields in \(R^ 2\) with nilpotent linear part. The investigation is divided in three subcases and except one subcase it is essentially complete. The paper has a high theoretical level, it applies the technics of Lie-algebras.

Reviewer: P.F.Moson (Budapest)

##### MSC:

34C23 | Bifurcation theory for ordinary differential equations |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

17B70 | Graded Lie (super)algebras |

##### Keywords:

normal forms; birfurcation; normalisation; unique formal classification of analytic vector fields in \(R^ 2\) with nilpotent linear part; Lie- algebras
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\textit{A. Baider} and \textit{J. A. Sanders}, J. Differ. Equations 99, No. 2, 205--244 (1992; Zbl 0761.34027)

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##### References:

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