RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2002, Volume 193, Number 11, Pages 105–124 (Mi msb693)  

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

Implicit differential equations and vector fields with non-isolated singular points

A. O. Remizov

M. V. Lomonosov Moscow State University

Abstract: Vector fields with singularities that are not isolated, but form a smooth submanifold of the phase space of codimension 2 are studied. Fields of this kind occur, for instance, in the analysis of implicit differential equations. Furthermore, under slight perturbations of the original problem the variety of singular points does not disappear or degenerate, but merely deforms. Results on the structure of invariant manifolds of such fields are obtained, along with smooth normal forms for certain cases.

DOI: https://doi.org/10.4213/sm693

Full text: PDF file (353 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2002, 193:11, 1671–1690

Bibliographic databases:

UDC: 517.922
MSC: 34A09, 37C10, 34C05, 34C20
Received: 23.01.2002

Citation: A. O. Remizov, “Implicit differential equations and vector fields with non-isolated singular points”, Mat. Sb., 193:11 (2002), 105–124; Sb. Math., 193:11 (2002), 1671–1690

Citation in format AMSBIB
\Bibitem{Rem02}
\by A.~O.~Remizov
\paper Implicit differential equations and vector fields with non-isolated singular points
\jour Mat. Sb.
\yr 2002
\vol 193
\issue 11
\pages 105--124
\mathnet{http://mi.mathnet.ru/msb693}
\crossref{https://doi.org/10.4213/sm693}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1937031}
\zmath{https://zbmath.org/?q=an:1082.34501}
\elib{http://elibrary.ru/item.asp?id=13408667}
\transl
\jour Sb. Math.
\yr 2002
\vol 193
\issue 11
\pages 1671--1690
\crossref{https://doi.org/10.1070/SM2002v193n11ABEH000693}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000181721200004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036875462}


Linking options:
  • http://mi.mathnet.ru/eng/msb693
  • https://doi.org/10.4213/sm693
  • http://mi.mathnet.ru/eng/msb/v193/i11/p105

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Sovrem. Mat. Prilozh., 2005, no. 36, 78–85  crossref  mathscinet  zmath  scopus
    2. V. M. Zakalyukin, A. O. Remizov, “Legendre Singularities in Systems of Implicit ODEs and Slow–Fast Dynamical Systems”, Proc. Steklov Inst. Math., 261 (2008), 136–148  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. Bonnard B., Glaser S.J., Sugny D., “A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance”, Adv. Math. Phys., 2012, 857493  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. Bonnard B., Chyba M., Marriott J., “Singular Trajectories and the Contrast Imaging Problem in Nuclear Magnetic Resonance”, SIAM J. Control Optim., 51:2 (2013), 1325–1349  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. Bernard Bonnard, Monique Chyba, Alain Jacquemard, John Marriott, “Algebraic geometric classification of the singular flow in the contrast imaging problem in nuclear magnetic resonance”, MCRF, 3:4 (2013), 397  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Bonnard B., Chyba M., Marriott J., “Feedback Equivalence and the Contrast Problem in Nuclear Magnetic Resonance Imaging”, Pac. J. Optim., 9:4, SI (2013), 635–650  mathscinet  zmath  isi
    7. Zhumatov S.S., “Asymptotic Stability of Implicit Differential Systems in the Vicinity of Program Manifold”, Ukr. Math. J., 66:4 (2014), 625–632  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:663
    Full text:188
    References:82
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019