Geodesic
An abstract reachability problem: “purely asymptotic” version
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 289-305 Cet article a éte moissonné depuis la source Math-Net.Ru

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A reachability problem in a topological space under constraints of asymptotic nature is considered. An extension construction using elements of compactification, as well as more general procedures employing generalized elements, is studied. The primary focus is on the case where exact solutions are absent. For this case, we study conditions for the realization of the set of admissible generalized elements in a remainder appearing under the immersion of the space of ordinary solutions. In particular, we specify conditions that provide such a realization in a remainder in the case of using (as generalized elements) ultrafilters of broadly understood measurable spaces.
Keywords: attraction set, topological space, ultrafilter. 
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A. G. Chentsov. An abstract reachability problem: “purely asymptotic” version. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 289-305. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a23/

[1] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp. | MR

[2] Daffin R.Dzh., “Beskonechnye programmy”, Lineinye neravenstva i smezhnye voprosy, IL, M., 1959, 263–267

[3] Golshtein E.G., Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya, Nauka, M., 1971, 351 pp. | MR

[4] Skvortsova A.V., Chentsov A.G., “O postroenii asimptoticheskogo analoga puchka traektorii lineinoi sistemy s odnoimpulsnym upravleniem”, Differents. uravneniya, 40:12 (2004), 1645–1657 | MR | Zbl

[5] Chentsov A.G., Baklanov A.P., “Ob odnoi zadache, svyazannoi s asimptoticheskoi dostizhimostyu v srednem”, Dokl. RAN, 459:6 (2014), 672–676 | DOI

[6] Aleksandryan R.A., Mirzakhanyan E.A., Obschaya topologiya, ucheb. posobie dlya vuzov, Vysshaya shkola, M., 1979, 336 pp.

[7] Chentsov A.G., Asymptotic attainability, Kluwer Acad. Publ., Dordrecht; Boston; London, 1997, 322 pp. | MR | Zbl

[8] Yang L., Lektsii po variatsionnomu ischisleniyu i teorii optimalnogo upravleniya, Mir, M., 1970, 488 pp. | MR

[9] Gamkrelidze R.V., Osnovy optimalnogo upravleniya, Izd-vo Tbilis. un-ta, Tbilisi, 1975, 230 pp. | MR

[10] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR

[11] Krasovskii N.N., Subbotin A.I., “Alternativa dlya igrovoi zadachi sblizheniya”, Prikl. matematika i mekhanika, 34:6 (1970), 1005–1022 | MR

[12] Arkhangelskii A.V., “Kompaktnost”, Itogi nauki i tekhniki (Sovremennye problemy matematiki. Fundamentalnye napravleniya), 50, 1989, 7–128 | MR

[13] Terpe F., Flaksmaier Yu., “O nekotorykh prilozheniyakh teorii rasshirenii topologicheskikh prostranstv i teorii mery”, Uspekhi mat. nauk, 32:5 (1977), 125–162 | MR | Zbl

[14] Chentsov A.G., “Ob odnom primere predstavleniya prostranstva ultrafiltrov algebry mnozhestv”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17:4 (2011), 293–311

[15] Chentsov A.G., “Mnozhestva prityazheniya v abstraktnykh zadachakh o dostizhimosti: ekvivalentnye predstavleniya i osnovnye svoistva”, Izv. vuzov. Matematika, 2013, no. 11, 33–50 | MR

[16] Chentsov A.G., “Nekotorye svoistva ultrafiltrov, svyazannye s konstruktsiyami rasshirenii”, Vestn. Udmurt. un-ta (Matematika, mekhanika, kompyuter. nauki), 2014, no. 1, 87–101 | Zbl

[17] Bulinskii A.V., Shiryaev A.N., Teoriya sluchainykh protsessov, Fizmatlit, M., 2005, 402 pp.

[18] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968, 272 pp. | MR

[19] Chentsov A.G., “Rasshireniya abstraktnykh zadach o dostizhimosti: nesekventsialnaya versiya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 13:2 (2007), 184–217

[20] Chentsov A.G., “The nonsequential approximate solutions in problems of asymptotic analysis”, Soochow Journal of Mathematics, 32:3 (2006), 441–475 | MR | Zbl

[21] Chentsov A.G., “Ultrafiltry v konstruktsiyakh mnozhestv prityazheniya: zadacha soblyudeniya ogranichenii asimptoticheskogo kharaktera”, Differents. uravneniya, 47:7 (2011), 1047–1064 | MR | Zbl

[22] Chentsov A.G., “K voprosu o strukture mnozhestv prityazheniya v topologicheskom prostranstve”, Izv. In-ta matematiki i informatiki Udmurt. un-ta, 2012, no. 1(39), 147–150 | MR

[23] Chentsov A.G., Baklanov A.P., “K voprosu o postroenii mnozhestva dostizhimosti pri ogranicheniyakh asimptoticheskogo kharaktera”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:3 (2014), 309–323

[24] Chentsov A.G., Elementy konechno-additivnoi teorii mery, I, Izd-vo UGTU-UPI, Ekaterinburg, 2009, 389 pp.

[25] Chentsov A.G., “K voprosu o soblyudenii ogranichenii v klasse obobschennykh elementov”, Vestn. Udmurt. un-ta(Matematika, mekhanika, kompyuter. nauki), 2014, no. 3, 90–109 | MR | Zbl