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Tr. Mat. Inst. Steklova, 2007, Volume 256, Pages 89–101 (Mi tm457)  

This article is cited in 2 scientific papers (total in 2 papers)

Structural Stability of Simplest Dynamical Inequalities

Yu. A. Grishinaa, A. A. Davydovab

a Vladimir State University
b International Institute for Applied Systems Analysis, Laxenburg, Austria

Abstract: The structural stability of families of orbits is proved for the simplest generic smooth dynamical inequality in the plane with bounded complement of the domain of complete controllability. Typical singularities of the boundaries of nonlocal transitivity zones for such inequalities are found. The stability of these singularities under small perturbations of the generic inequality is proved.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 256, 80–91

Bibliographic databases:

UDC: 517.9
Received in June 2006

Citation: Yu. A. Grishina, A. A. Davydov, “Structural Stability of Simplest Dynamical Inequalities”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Tr. Mat. Inst. Steklova, 256, Nauka, MAIK Nauka/Inteperiodika, M., 2007, 89–101; Proc. Steklov Inst. Math., 256 (2007), 80–91

Citation in format AMSBIB
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\by Yu.~A.~Grishina, A.~A.~Davydov
\paper Structural Stability of Simplest Dynamical Inequalities
\inbook Dynamical systems and optimization
\bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov
\serial Tr. Mat. Inst. Steklova
\yr 2007
\vol 256
\pages 89--101
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
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\zmath{https://zbmath.org/?q=an:1167.34021}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
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\crossref{https://doi.org/10.1134/S0081543807010051}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248346706}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. Davydov A., “Normal Forms of Linear Second Order Partial Differential Equations on the Plane”, Sci. China-Math., 61:11, SI (2018), 1947–1962  crossref  mathscinet  zmath  isi  scopus
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