Geodesic
Generic Profit Singularities in Arnold's Model of Cyclic Processes
Informatics and Automation, Differential equations and dynamical systems, Tome 250 (2005), pp. 79-94

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2005_250_a3,
     author = {A. A. Davydov},
     title = {Generic {Profit} {Singularities} in {Arnold's} {Model} of {Cyclic} {Processes}},
     journal = {Informatics and Automation},
     pages = {79--94},
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     volume = {250},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2005_250_a3/}
}
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A. A. Davydov. Generic Profit Singularities in Arnold's Model of Cyclic Processes. Informatics and Automation, Differential equations and dynamical systems, Tome 250 (2005), pp. 79-94. http://geodesic.mathdoc.fr/item/TRSPY_2005_250_a3/