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Matematicheskie Zametki, 1998, Volume 64, Issue 4, Pages 531–542
DOI: https://doi.org/10.4213/mzm1427 (Mi mzm1427) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Local singularities of dynamical systems with shock interactions

S. P. Gorbikov

Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
Full-text PDF (1340 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm1427
Abstract: Local (qualitative) singularities of a special class of dynamical systems with shock interactions are classified. For the first four of the specified types of local singularities, certain properties of the qualitative structure are described and used to establish the topological equivalence of the corresponding singularities.
Received: 26.09.1995
Revised: 28.01.1998
English version:
Mathematical Notes, 1998, Volume 64, Issue 4, Pages 461–470
DOI: https://doi.org/10.1007/BF02314626
Bibliographic databases:
UDC: 517.938.5
Language: Russian
Citation: S. P. Gorbikov, “Local singularities of dynamical systems with shock interactions”, Mat. Zametki, 64:4 (1998), 531–542; Math. Notes, 64:4 (1998), 461–470
Citation in format AMSBIB
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\by S.~P.~Gorbikov
\paper Local singularities of dynamical systems with shock interactions
\jour Mat. Zametki
\yr 1998
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\issue 4
\pages 531--542
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\transl
\jour Math. Notes
\yr 1998
\vol 64
\issue 4
\pages 461--470
\crossref{https://doi.org/10.1007/BF02314626}
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Linking options:
  • https://www.mathnet.ru/eng/mzm1427
  • https://doi.org/10.4213/mzm1427
  • https://www.mathnet.ru/eng/mzm/v64/i4/p531
    • This publication is cited in the following 6 articles:
    1. S. P. Gorbikov, “Auxiliary sliding motions of vibro-impact systems”, Autom. Remote Control, 81:8 (2020), 1413–1430  mathnet  crossref  crossref  isi  elib  elib
    2. Otstavnov E.I., “Issledovanie ustoichivosti nepodvizhnykh tochek sistem s transversalnym odnostoronnim ogranicheniem”, Vestnik MGSU, 2011, no. 4, 253–253 Fixed points stability investigation for systems with transversal one-sided restrictions  elib
    3. Otstavnov E.I., “Issledovanie ustoichivosti nepodvizhnykh tochek sistem s kasatelnym odnostoronnim ogranicheniem po pervomu priblizheniyu”, Vestnik MGSU, 2011, no. 4, 260–260 Linear approximation fixed points stability investigation of systems with tangent one-sided restrictions  elib
    4. S. P. Gorbikov, A. V. Men'shenina, “Statistical description of the limiting set for chaotic motions of the vibro-impact system”, Autom. Remote Control, 68:10 (2007), 1794–1800  mathnet  crossref  mathscinet  zmath
    5. Gorbikov, SP, “Bifurcation resulting in chaotic motions in dynamical systems with shock interactions”, Differential Equations, 41:8 (2005), 1097  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. S. P. Gorbikov, “Topological Equivalence of Local Singularities of Particular Type for Dynamical Systems with Shock Interactions”, Math. Notes, 70:2 (2001), 163–174  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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