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Trudy Inst. Mat. i Mekh. UrO RAN, 2006, Volume 12, Number 1, Pages 216–241 (Mi timm145)  

This article is cited in 14 scientific papers (total in 14 papers)

Nonsequential approximate solutions in abstract problems of attainability

A. G. Chentsov


Abstract: The problem of constructing attraction sets in a topological space is considered in the case when the choice of the asymptotic version of the solution is subject to constraints in the form of a nonempty family of sets. Each of these sets must contain an “almost entire” solution (for example, all elements of the sequence, starting from some number, when solution-sequences are used). In the paper, problems of the structure of the attraction set are investigated. The dependence of attraction sets on the topology and the family determining “asymptotic” constraints is considered. Some issues concerned with the application of Stone–Čech compactification and the Wallman extension are investigated.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2006, 253, suppl. 1, S48–S75

Bibliographic databases:

Document Type: Article
UDC: 517.972.8
Received: 21.11.2005

Citation: A. G. Chentsov, “Nonsequential approximate solutions in abstract problems of attainability”, Dynamical systems: modeling, optimization, and control, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 1, 2006, 216–241; Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S48–S75

Citation in format AMSBIB
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\paper Nonsequential approximate solutions in abstract problems of attainability
\inbook Dynamical systems: modeling, optimization, and control
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 1
\pages 216--241
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 253
\issue , suppl. 1
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\crossref{https://doi.org/10.1134/S0081543806050051}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Chentsov, “Extensions of abstract problems of attainability: Nonsequential version”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S46–S82  mathnet  crossref  elib
    2. A. G. Chentsov, “Construction of limiting process operations using ultrafilters of measurable spaces”, Autom. Remote Control, 68:11 (2007), 2083–2096  mathnet  crossref  mathscinet  zmath  elib  elib
    3. Chentsov A.G., “The space of stone representation and construction of extensions”, Dokl. Math., 75:2 (2007), 314–317  crossref  zmath  isi  elib  scopus
    4. A. G. Chentsov, “Extension of the abstract attainability problem using the Stone representation space”, Russian Math. (Iz. VUZ), 52:3 (2008), 58–68  mathnet  crossref  mathscinet  zmath  elib
    5. A. G. Chentsov, “Prostranstvo stounovskogo predstavleniya i konstruktsii rasshirenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 2, 169–172  mathnet
    6. A. G. Chentsov, “On the result equivalence of constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S32–S53  mathnet  crossref  isi  elib
    7. S. I. Tarasova, “The closure of the sheaf of trajectories of a linear control system with integral constraints”, Russian Math. (Iz. VUZ), 53:12 (2009), 50–58  mathnet  crossref  mathscinet  zmath
    8. A. G. Chentsov, “Rasshireniya v klasse konechno-additivnykh mer i usloviya asimptoticheskoi nechuvstvitelnosti pri oslablenii chasti ogranichenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 1, 131–152  mathnet
    9. A. G. Chentsov, “Ultrafilters of measurable spaces as generalized solutions in abstract attainability problems”, Proc. Steklov Inst. Math. (Suppl.), 275, suppl. 1 (2011), S12–S39  mathnet  crossref  isi  elib
    10. A. G. Chentsov, “Filtry i ultrafiltry v konstruktsiyakh mnozhestv prityazheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 1, 113–142  mathnet
    11. A. G. Chentsov, “One representation of the results of action of approximate solutions in a problem with constraints of asymptotic nature”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S48–S62  mathnet  crossref  isi  elib
    12. Chentsov A.G., “Ultrafilters in the constructions of attraction sets: problem of compliance to constraints of asymptotic character”, Differ. Equ., 47:7 (2011), 1059–1076  crossref  mathscinet  zmath  isi  elib  elib  scopus
    13. A. G. Chentsov, “Representation of attraction elements in abstract attainability problems with asymptotic constraints”, Russian Math. (Iz. VUZ), 56:10 (2012), 38–49  mathnet  crossref  mathscinet
    14. A. G. Chentsov, “K voprosu o soblyudenii ogranichenii v klasse obobschennykh elementov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 3, 90–109  mathnet
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