Geodesic
On the alternating integral of Pontryagin
Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 125-132 
M. S. Nikol'skii. On the alternating integral of Pontryagin. Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 125-132. http://geodesic.mathdoc.fr/item/SM_1983_44_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Pontryagin introduced the notion of alternating integral to solve linear differential games of pursuit. To construct this integral one uses, in particular, Riemann integration of certain multivalued mappings. Pontryagin posed the problem of constructing an alternating integral in such a way that the operation of integrating multivalued mappings is absent. One of the possible methods of such a construction is presented in this paper. Bibliography: 6 titles.

[1] Pontryagin L. S., “O lineinykh differentsialnykh igrakh. 2”, DAN SSSR, 175:4 (1967), 764–766 | Zbl

[2] Pontryagin L. S., “Lineinye differentsialnye igry presledovaniya”, Matem. sb., 112 (154) (1980), 307–330 | MR | Zbl

[3] Materon Zh., Sluchainye mnozhestva i integralnaya geometriya, Mir, M., 1978 | MR

[4] Nikolskii M. S., “Nestatsionarnye lineinye differentsialnye igry”, Vestnik MGU, ser. 1, matem., mekhanika, 1969, no. 3, 65–73

[5] Polovinkin E. S., “Neavtonomnye differentsialnye igry”, Diff. uravneniya, XV:6 (1979), 1007–1017 | MR

[6] Pshenichnyi B. P., Sagaidak M. I., “O differentsialnykh igrakh s fiksirovannym vremenem”, Kibernetika, 1970, no. 2, 54–63 | MR