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Tr. Mat. Inst. Steklova, 2008, Volume 262, Pages 73–86 (Mi tm766)  

This article is cited in 7 scientific papers (total in 7 papers)

Envelope Singularities of Families of Planes in Control Theory

V. M. Zakalyukinab, A. N. Kurbatskiia

a M. V. Lomonosov Moscow State University
b University of Liverpool

Abstract: Generic singularities of the local transitivity set for control systems with nonconvex indicatrix on three-dimensional manifolds are classified. A simple recognition criterion for generic singularities of envelopes of bi-tangents to space curves is described.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 262, 66–79

Bibliographic databases:

UDC: 517.988+519.71
Received in April 2008

Citation: V. M. Zakalyukin, A. N. Kurbatskii, “Envelope Singularities of Families of Planes in Control Theory”, Optimal control, Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday, Tr. Mat. Inst. Steklova, 262, MAIK Nauka/Interperiodica, Moscow, 2008, 73–86; Proc. Steklov Inst. Math., 262 (2008), 66–79

Citation in format AMSBIB
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\paper Envelope Singularities of Families of Planes in Control Theory
\inbook Optimal control
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\pages 73--86
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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. 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
    2. 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
    3. A. N. Kurbatskii, “Convex hulls of a curve in control theory”, Sb. Math., 203:3 (2012), 406–423  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. A. Davydov, V. M. Zakalyukin, “Controllability of non-linear systems: generic singularities and their stability”, Russian Math. Surveys, 67:2 (2012), 255–280  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Nuno Ballesteros J.J., “Unfolding Plane Curves With Cusps and Nodes”, Proc. R. Soc. Edinb. Sect. A-Math., 145:1 (2015), 161–174  crossref  mathscinet  zmath  isi  scopus
    6. A. A. Uspenskii, P. D. Lebedev, “Vyyavlenie singulyarnosti u obobschennogo resheniya zadachi Dirikhle dlya uravneniya tipa eikonala v usloviyakh minimalnoi gladkosti granitsy kraevogo mnozhestva”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 59–73  mathnet  crossref  elib
    7. Ishikawa G., “Singularities of Frontals”, Singularities in Generic Geometry, Advanced Studies in Pure Mathematics, 78, ed. Izumiya S. Ishikawa G. Yamamoto M. Saji K. Yamamoto T. Takahashi M., Math Soc Japan, 2018, 55–106  crossref  mathscinet  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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