This article is cited in 15 papers

Generic phase transitions and profit singularities in Arnol'd's model

A. A. Davydov^ab, H. Mena Matos<sup>c

a</sup> Vladimir State University
^b International Institute for Applied Systems Analysis
^c University of Porto

Abstract: 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.

UDC: 517.9

MSC: Primary 49J15; Secondary 49J45, 49N20, 49N60, 58K25, 58K40, 90C31

Received: 18.11.2005 and 17.10.2006

DOI: 10.4213/sm1438

 English version: Sbornik: Mathematics, 2007, 198:1, 17–37

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