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Consider in R2 the semi-planes N = { y > 0} and S = { y < 0} having as common bo u nda r y the s t r a i ght line D = { y = 0} . In N and S are de fi ned l i nea r vecto r fi elds X and Y , respectively, leading to a discontinuous polynomial vector field Z = ( X, Y ) . If the vector fields X and Y satisfy suitable conditions, they produce a transition flow from a segment of the splitting line to another segment and this produces a generalized singular point on the line. This point can be a focus or a center. In this paper we give necessary and sufficient conditions to a D -singular point be a monodromic.

The monodromic singularity to piecewise linear vector fields