Investigation of a 3D system of differential equations with non-isolated singular points

A system of the family, considered in the papers of A.O. Remizov, is investigated. For all the fields of the family, the origin is a non-isolated singular point of a complicated nature (the linear part of the field at the singular point can have the type "nilpotent Jordan cell" ). It was shown by A.O. Remizov (with coauthors) that for the considered vector fields there exists one-parametric family of the phase curves entering into the singular point; for a certain case there is also one additional phase curve with the same property. In the present paper we consider one of the vector fields of the Remizov family, apparently not studied previously. For this vector field analogous results to the pointed above are obtained.