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Sbornik: Mathematics, 2007, Volume 198, Issue 1, Pages 17–37
DOI: https://doi.org/10.1070/SM2007v198n01ABEH003827
(Mi sm1438)
 

This article is cited in 15 scientific papers (total in 15 papers)

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

A. A. Davydovab, H. Mena Matosc

a Vladimir State University
b International Institute for Applied Systems Analysis
c University of Porto
References:
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.
Received: 18.11.2005 and 17.10.2006
Bibliographic databases:
UDC: 517.9
MSC: Primary 49J15; Secondary 49J45, 49N20, 49N60, 58K25, 58K40, 90C31
Language: English
Original paper language: Russian
Citation: A. A. Davydov, H. Mena Matos, “Generic phase transitions and profit singularities in Arnol'd's model”, Sb. Math., 198:1 (2007), 17–37
Citation in format AMSBIB
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\by A.~A.~Davydov, H.~Mena Matos
\paper Generic phase transitions and profit singularities in Arnol'd's model
\jour Sb. Math.
\yr 2007
\vol 198
\issue 1
\pages 17--37
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Linking options:
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  • https://doi.org/10.1070/SM2007v198n01ABEH003827
  • https://www.mathnet.ru/eng/sm/v198/i1/p21
  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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