Geodesic
Generic phase transitions and profit singularities in Arnol'd's model
Sbornik. Mathematics, Tome 198 (2007) no. 1, pp. 17-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a smooth one-parameter family of pairs of control systems and profit densities on a circle, the generic transitions between optimal rotations and stationary strategies are studied in the problem of maximization of the time-averaged profit on the infinite horizon. It is shown that there are only two types of such transitions, the corresponding singularities of the average profit as a function of the family parameter are found, and it is proved that these singularities are stable under small perturbations of a generic family. The classification of singularities of the maximum average profit is completed for generic families. Bibliography: 16 titles. 
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A. A. Davydov; H. Mena Matos. Generic phase transitions and profit singularities in Arnol'd's model. Sbornik. Mathematics, Tome 198 (2007) no. 1, pp. 17-37. http://geodesic.mathdoc.fr/item/SM_2007_198_1_a1/

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