The paper presents a complete characterization of the local dynamics for optimal control problems of 4-dimensional systems of ordinary differential equations, by using geometrical methods. We prove that the particular structure of the Jacobian implies that the 8 th order characteristic...

The paper treats a noncooperative game where an upstream firm and two downstream firms select locations in a spatial system made by two asymmetric countries. The location of the upstream firm is indeterminate and it is assigned to the smaller country, in order to avoid triviality of the location...