Geodesic
Phenomenon of narrow throats of level sets of value function in~differential games
Contributions to game theory and management, Tome 7 (2014), pp. 159-180

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A number of zero-sum differential games with fixed termination instant are given, in which a level set of the value function has one or more time sections that are almost degenerated (have no interior). Presence of such a peculiarity make very high demands on the accuracy of computational algorithms for constructing value function. Analysis and causes of these degeneration situations are important during study of applied pursuit problems.
Keywords: linear differential games, fixed termination instant, level sets of value function, geometric methods, narrow throats. 
@article{CGTM_2014_7_a14,
     author = {Sergey S. Kumkov and Valerii S. Patsko},
     title = {Phenomenon of narrow throats of level sets of value function in~differential games},
     journal = {Contributions to game theory and management},
     pages = {159--180},
     publisher = {mathdoc},
     volume = {7},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2014_7_a14/}
}
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Sergey S. Kumkov; Valerii S. Patsko. Phenomenon of narrow throats of level sets of value function in~differential games. Contributions to game theory and management, Tome 7 (2014), pp. 159-180. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a14/