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Algebra i Analiz, 2010, Volume 22, Issue 2, Pages 127–163 (Mi aa1179)  
This article is cited in 6 scientific papers (total in 6 papers)

Research Papers

Nondensity of the orbital shadowing property in $C^1$-topology

A. V. Osipov

St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia
Full-text PDF (758 kB) Citations (6)
References:
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Abstract: The orbital shadowing property (OSP) of discrete dynamical systems on smooth closed manifolds is considered. The nondensity of OSP with respect to the $C^1$-topology is proved. The proof uses the method of skew products developed by Ilyashenko and Gorodetskiĭ.
Keywords: shadowing, generic property, skew product, $C^1$-topology.
Received: 28.02.2009
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 2, Pages 267–292
DOI: https://doi.org/10.1090/S1061-0022-2011-01140-9
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Osipov, “Nondensity of the orbital shadowing property in $C^1$-topology”, Algebra i Analiz, 22:2 (2010), 127–163; St. Petersburg Math. J., 22:2 (2011), 267–292
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/aa1179
  • https://www.mathnet.ru/eng/aa/v22/i2/p127
    • This publication is cited in the following 6 articles:
    1. Lee M., “Orbital Shadowing Property on Chain Transitive Sets For Generic Diffeomorphisms”, Acta Univ. Sapientiae-Math., 12:1 (2020), 146–154  crossref  mathscinet  isi
    2. Gan Sh., Li M., “Orbital shadowing for 3-flows”, J. Differ. Equ., 262:10 (2017), 5022–5051  crossref  mathscinet  zmath  isi  scopus
    3. Ilyashenko Yu., Shilin I., “Attractors and Skew Products”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. Katok A., Pesin Y., Hertz F., Amer Mathematical Soc, 2017, 155–175  crossref  mathscinet  zmath  isi  scopus
    4. Lee M., “Orbital Shadowing Property for Generic Divergence-Free Vector Fields”, Chaos Solitons Fractals, 54 (2013), 71–75  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Pilyugin S.Yu., “Theory of pseudo-orbit shadowing in dynamical systems”, Differ. Equ., 47:13 (2011), 1929–1938  crossref  mathscinet  zmath  isi  elib  scopus
    6. V. A. Kleptsyn, P. S. Saltykov, “On $C^2$-stable effects of intermingled basins of attractors in classes of boundary-preserving maps”, Trans. Moscow Math. Soc., 72 (2011), 193–217  mathnet  crossref  zmath  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:492
    Full-text PDF :100
    References:70
    First page:15
     
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