Generic Profit Singularities in Arnold's Model of Cyclic Processes

Generic singularities of the maximum time-averaged profit are classified for a one-parameter smooth pair of families of profit densities and control systems with positive velocities on the circle. For example, a typical passage of this profit through a local nondegenerate extremum of the profit density under the change of the parameter yields the singularity $(|p|^{3/2}\pm \nobreak p^2)(1+\mathop {\mathrm {sgn}} p)$ of the profit up to a diffeomorphism of its graph space fibered over the parameter.