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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 4(8), Pages 478–499 (Mi msb1755)  

This article is cited in 13 scientific papers (total in 13 papers)

Singularities of fields of limiting directios of two-dimensional control systems

A. A. Davydov


Abstract: The singularities of the fields of limiting directions of two-dimensional control systems in general position are classified, and it is proved that these singularities are stable under small perturbations of such systems.
Tables: 2.
Figures: 2.
Bibliography: 17 titles.

Full text: PDF file (1434 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 471–493

Bibliographic databases:

UDC: 517.9
MSC: Primary 58C27, 57R45; Secondary 34K35, 58A20, 34C05, 49A10, 49E99
Received: 21.01.1987

Citation: A. A. Davydov, “Singularities of fields of limiting directios of two-dimensional control systems”, Mat. Sb. (N.S.), 136(178):4(8) (1988), 478–499; Math. USSR-Sb., 64:2 (1989), 471–493

Citation in format AMSBIB
\Bibitem{Dav88}
\by A.~A.~Davydov
\paper Singularities of fields of limiting directios of two-dimensional control systems
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 4(8)
\pages 478--499
\mathnet{http://mi.mathnet.ru/msb1755}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=965888}
\zmath{https://zbmath.org/?q=an:0714.58040}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 2
\pages 471--493
\crossref{https://doi.org/10.1070/SM1989v064n02ABEH003321}


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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. A. Davydov, “Structural stability of control systems on orientable surfaces”, Math. USSR-Sb., 72:1 (1992), 1–28  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Davydov, J. Basto-Gonçalves, “Local controllability of generic dynamic inequalities”, Journal of Mathematical Sciences (New York), 135:4 (2006), 3145  crossref  mathscinet  elib
    3. Jakubczyk B., Respondek W., “Bifurcations of 1-Parameter Families of Control-Affine Systems in the Plane”, SIAM J. Control Optim., 44:6 (2006), 2038–2062  crossref  mathscinet  zmath  isi
    4. Rupniewski M.W., “Local Bifurcations of Control-Affine Systems in the Plane”, J. Dyn. Control Syst., 13:1 (2007), 135–159  crossref  mathscinet  zmath  isi
    5. A. A. Davydov, M. A. Komarov, “Local Controllability Bifurcations in Families of Bidynamical Systems on the Plane”, Proc. Steklov Inst. Math., 261 (2008), 84–93  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. V. M. Zakalyukin, A. N. Kurbatskii, “Convex hulls of surfaces with boundaries and corners and singularities of transitivity zone in $\mathbb R^3$”, Proc. Steklov Inst. Math., 268 (2010), 274–293  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. A. N. Kurbatskii, “Singularities of the transitivity zone of surfaces with boundaries in $\mathbb R^3$”, Russian Math. Surveys, 65:3 (2010), 583–585  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Rupniewski M.W., Respondek W., “A Classification of Generic Families of Control-Affine Systems and their Bifurcations”, Math. Control Signal Syst., 21:4 (2010), 303–336  crossref  mathscinet  zmath  isi
    9. M. A. Komarov, “Structure of the local controllability set for a family of $2$-systems on a plane near the zero indicatrix point”, Journal of Mathematical Sciences, 199:6 (2014), 667–686  mathnet  crossref  mathscinet
    10. Hy Ðú'c Mạnh, “Stability of local transitivity of a generic control system on a surface with boundary”, Proc. Steklov Inst. Math., 278 (2012), 260–266  mathnet  crossref  mathscinet  isi
    11. A. A. Davydov, Hy Duc Manh, “Singularities of the attainable set on an orientable surface with boundary”, J Math Sci, 2012  crossref
    12. V. M. Zakalyukin, A. N. Kurbatskii, “Convex hulls of indicatrices and singularities of the transitivity zone in $ {{\mathbb{R}}^3} $”, J Math Sci, 2013  crossref
    13. H.D.uc Manh, “Generic Singularities of the Attainable Set on Surfaces with Boundary”, J Math Sci, 2014  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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