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Mat. Sb., 1990, Volume 181, Number 5, Pages 579–588 (Mi msb1190)  

This article is cited in 3 scientific papers (total in 4 papers)

The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable

A. Yu. Kolesova, E. F. Mishchenkob

a P. G. Demidov Yaroslavl State University
b V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: It is assumed that the equilibrium state of the relaxation system
$$ \varepsilon\dot x=f(x,y), \qquad \dot y=g(x,y,\mu), $$
where $x\in R^n$ and $y\in R$, passes generically through a point of discontinuity as $\mu$ varies. Under this condition stable duck cycles and cycles arising in a neighborhood of the equilibrium state are constructed.

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English version:
Mathematics of the USSR-Sbornik, 1991, 70:1, 1–10

Bibliographic databases:

UDC: 517.926
MSC: Primary 34D15, 34C25; Secondary 34C45, 34E05, 34C20
Received: 17.11.1989

Citation: A. Yu. Kolesov, E. F. Mishchenko, “The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable”, Mat. Sb., 181:5 (1990), 579–588; Math. USSR-Sb., 70:1 (1991), 1–10

Citation in format AMSBIB
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\by A.~Yu.~Kolesov, E.~F.~Mishchenko
\paper The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable
\jour Mat. Sb.
\yr 1990
\vol 181
\issue 5
\pages 579--588
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\zmath{https://zbmath.org/?q=an:0731.34028}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991SbMat..70....1K}
\transl
\jour Math. USSR-Sb.
\yr 1991
\vol 70
\issue 1
\pages 1--10
\crossref{https://doi.org/10.1070/SM1991v070n01ABEH002117}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GG78300001}


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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. Kolesov A. Rozov N., “Cycles-Ducks of Three-Dimensional Relaxation Systems with a Fast Variable and Two Slow Variables”, Differ. Equ., 32:2 (1996), 181–185  mathnet  mathscinet  zmath  isi
    2. A. Yu. Kolesov, N. Kh. Rozov, “The “Buridan's Ass” problem in relaxation systems with one slow variable”, Math. Notes, 65:1 (1999), 128–131  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. N. A. Arzhanova, M. A. Prokaznikov, A. V. Prokaznikov, “Self-organization process under electrolytic formation of nanostructures in silicon-based semi-conducting systems”, Russ Microelectron, 43:6 (2014), 413  crossref
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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