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On the normal form of a system of differential equations with nilpotent linear part. (English. Abridged French version) Zbl 1036.34105

Summary: We consider prenormal forms associated to generic perturbations of the system \(\dot x= 2y\), \(\dot y= 3x^2\). It is known that they have a formal normal form \(\dot x= 2y+ 2x\Delta^*\), \(\dot y= 3x^2+ 3y\Delta^*\), with \(\Delta^*= x+ A_0(y^2- x^3)\) [see F. Loray, J. Differ. Equations 158, 152–173 (1999; Zbl 0985.37014)]. We show that the series \(A_0\) and the normalizing transformations are divergent, but 1-summable.

MSC:

34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms

Citations:

Zbl 0985.37014
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References:

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