The Topological Structure of the Phase Portrait of a Typical Fiber of Optimal Synthesis for Chattering Problems

This paper continues the program of optimal chattering synthesis design for problems with a multidimensional control. In contrast to the paper where the case of independent constraints on different components of the control was explored, here the control takes its values in a two-dimensional simplex. In this case, one again deals with integral varieties like the Reeb foliation; however, the inclusion of these varieties in the phase space is much more exotic. This paper is devoted to the description of the corresponding phase portrait.