Geodesic
Mappings conjugate to multivalued mappings of topological spaces, and their application to dynamical games
Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 323-331 
V. A. Baidosov. Mappings conjugate to multivalued mappings of topological spaces, and their application to dynamical games. Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 323-331. http://geodesic.mathdoc.fr/item/SM_1990_65_2_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Associated with multivalued mappings of a topological space $X$ into a topological space $Y$ are conjugate mappings of the set of upper (lower) semicontinuous real functions on $Y$ into the set of real functions on $X$. It is shown that to compactvalued upper semicontinuous mappings of $X$ into $Y$ there correspond mappings of the set of upper (lower) semicontinuous real functions on $Y$ into the set of upper (lower) semicontinuous real functions on $X$. The properties of the conjugate mappings are studied, and their applications to dynamical games are considered. Bibliography: 7 titles.

[1] Kuratovskii K., Topologiya, T. 1, Mir, M., 1966 | MR

[2] Burbaki N., Obschaya topologiya. Chisla i svyazannye s nimi gruppy i prostranstva, Gos. izd-vo fiz.-matem. lit., M., 1959 | MR

[3] Borisovich Yu. G., Gelman V. D., Myshkis A. D., Obukhovskii V. V., “Mnogoznachnye otobrazheniya”, Itogi nauki i tekhniki. Matematicheskii analiz, 19, VINITI, M., 1982, 127–230 | MR

[4] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR

[5] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1988 | MR | Zbl

[6] Roxin E., “Stability in control systems”, J. Different. Equat., 1:2 (1965), 115–150 | DOI | MR | Zbl

[7] Baidosov V. A., “O podkhode k opredeleniyu dinamicheskikh igr na yazyke obobschennykh dinamicheskikh sistem”, Optimalnoe upravlenie sistemami s neopredelennoi informatsiei, UNTs AN SSSR, Sverdlovsk, 1980, 3–11 | MR