On the inverse problems of the polynomial vector fields in R3

In this paper, we deduce the normal forms of polynomial differential systems in R-3 having, Fermat cubic surface, Clebsch surface, Goursat surface, Racor surface and 2-dimensional tours as invariant objects. We prove if we have an odd number of polynomial differential equations with the determined inverse Jacobian multipliers then we can make a new polynomial differential system of the first systems so that it's inverse Jacobian multiplier can be determined by the inverse Jacobian multipliers of the first systems. If new system which is made by them has a limit cycle then we determine it's position.