We consider non-linear holomorphic vector fields Z defined in an open U of C2 wíth isolated singularity at the origin. We study a system of differential equations associated to the vector field Z, for the case in which the linear part of this field ís in Siegel' s domain. The concept of holonomy is used.

Se consideran dos campos vectoriales analíticos del tipo: ...

Un sistema no hiperbólico en el plano, tal como...puede presentar el caso en que la matriz de la parte lineal tenga un autovalor cero o los dos autovalores nulos. En tales casos es necesario conocer el comportamiento de las trayectorias en la vecindad de un punto singular aislado. En éste trabajo se analiza la situación cuando la matriz tiene sus dos autovalores nulos.

Already in the article [5] we consider the not hiperbolic system which is transformed inand analyze the case when k is an odd number. In the present article will analyzethe behaviour of the trajectories in the vicinity of a isolated singular point , when kis a number pair. 

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We consider non-linear holomorphic vector fields Z defined in an open U of C2 wíth isolated singularity at the origin. We study a system of differential equations associated to the vector field Z, for the case in which the linear part of this field ís in Siegel' s domain. The concept of holonomy is used.

Se consideran dos campos vectoriales analíticos del tipo: ...

Un sistema no hiperbólico en el plano, tal como...puede presentar el caso en que la matriz de la parte lineal tenga un autovalor cero o los dos autovalores nulos. En tales casos es necesario conocer el comportamiento de las trayectorias en la vecindad de un punto singular aislado. En éste trabajo se analiza la situación cuando la matriz tiene sus dos autovalores nulos.

En el artículo [5] se consideró el sistema no hiperbólico ...el cual se transforma en ...y se analizó el caso para cuando k es impar. En el presente artículo analizaremos el comportamiento de las trayectorias en la vecindad de un punto singular aisladocuando k es par.