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Uspekhi Mat. Nauk, 1989, Volume 44, Issue 6(270), Pages 3–28 (Mi umn1947)  

This article is cited in 27 scientific papers (total in 27 papers)

Small perturbations of chaotic dynamical systems

M. L. Blank


Full text: PDF file (2020 kB)
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English version:
Russian Mathematical Surveys, 1989, 44:6, 1–33

Bibliographic databases:

UDC: 519.25
MSC: 37D45, 37D50, 37D10, 28C10
Received: 07.02.1989

Citation: M. L. Blank, “Small perturbations of chaotic dynamical systems”, Uspekhi Mat. Nauk, 44:6(270) (1989), 3–28; Russian Math. Surveys, 44:6 (1989), 1–33

Citation in format AMSBIB
\Bibitem{Bla89}
\by M.~L.~Blank
\paper Small perturbations of chaotic dynamical systems
\jour Uspekhi Mat. Nauk
\yr 1989
\vol 44
\issue 6(270)
\pages 3--28
\mathnet{http://mi.mathnet.ru/umn1947}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1037009}
\zmath{https://zbmath.org/?q=an:0702.58063}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1989RuMaS..44S...1B}
\transl
\jour Russian Math. Surveys
\yr 1989
\vol 44
\issue 6
\pages 1--33
\crossref{https://doi.org/10.1070/RM1989v044n06ABEH002302}


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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. M. L. Blank, “Marginal singularities, almost invariant sets, and small perturbations of chaotic dynamical systems”, Chaos, 1:3 (1991), 347  crossref  mathscinet  zmath  adsnasa
    2. Ya. G. Sinai, “Finite-dimensional randomness”, Russian Math. Surveys, 46:3 (1991), 177–190  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. E. A. Sataev, “Invariant measures for hyperbolic maps with singularities”, Russian Math. Surveys, 47:1 (1992), 191–251  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Jörn Loviscach, “Probabilistic models of multidimensional piecewise expanding mappings”, J Statist Phys, 75:1-2 (1994), 189  crossref  mathscinet  zmath  adsnasa  isi
    5. V. I. Bakhtin, “Random processes generated by a hyperbolic sequence of mappings. I”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 247–279  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Phil Diamond, Aleksej Pokrovskii, “Chaos, entropy and a generalized extension principle”, Fuzzy Sets and Systems, 61:3 (1994), 277  crossref
    7. Franco Vivaldi, “Periodicity and Transport from Round-Off Errors”, Experimental Mathematics, 3:4 (1994), 303  crossref
    8. Phil Diamond, Peter Kloeden, Aleksej Pokrovskii, “Interval stochastic matrices: A combinatorial lemma and the computation of invariant measures of dynamical systems”, J Dyn Diff Equat, 7:2 (1995), 341  crossref  mathscinet  zmath
    9. Hua O. Wang, Eyad H. Abed, “Bifurcation control of a chaotic system”, Automatica, 31:9 (1995), 1213  crossref  elib
    10. Leonid A. Bunimovich, “Coupled map lattices: one step forward and two steps back”, Physica D: Nonlinear Phenomena, 86:1-2 (1995), 248  crossref
    11. Phil Diamond, Peter Kloeden, Alexei Pokrovskii, “Analysis of an algorithm for computing invariant measures”, Nonlinear Analysis: Theory, Methods & Applications, 24:3 (1995), 323  crossref
    12. N. Kuznetsov, P. Kloeden, “The problem of information stability in computer studies of continuous systems”, Mathematics and Computers in Simulation, 43:2 (1997), 143  crossref
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    17. D. I. Sementsov, A. M. Shutyi, “Nonlinear regular and stochastic dynamics of magnetization in thin-film structures”, Phys. Usp., 50:8 (2007), 793–818  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    18. Rongbao Gu, “The asymptotic average shadowing property and transitivity”, Nonlinear Analysis: Theory, Methods & Applications, 67:6 (2007), 1680  crossref
    19. Rongbao Gu, “The average-shadowing property and topological ergodicity”, Journal of Computational and Applied Mathematics, 206:2 (2007), 796  crossref
    20. Rongbao Gu, “On ergodicity of systems with the asymptotic average shadowing property”, Computers & Mathematics with Applications, 55:6 (2008), 1137  crossref
    21. Bashkirtseva I.A., Karpenko L.V., Ryashko L.B., “Analiz attraktorov stokhasticheski vozmuschennoi modeli «khischnik-zhertva»”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 17:2 (2009), 37–53  elib
    22. Yingxuan Niu, “The average-shadowing property and strong ergodicity”, Journal of Mathematical Analysis and Applications, 376:2 (2011), 528  crossref
    23. Stefano Galatolo, Mathieu Hoyrup, Cristóbal Rojas, “Statistical properties of dynamical systems – Simulation and abstract computation”, Chaos, Solitons & Fractals, 2011  crossref
    24. Risong Li, Xiaoliang Zhou, “A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property”, Discrete Dynamics in Nature and Society, 2011 (2011), 1  crossref
    25. Manseob Lee, Xiao Wen, “Diffeomorphisms with C 1-stably average shadowing”, Acta. Math. Sin.-English Ser, 2012  crossref
    26. Yi Wang, Y.X.uan Niu, “Strong ergodicity of systems with the average shadowing property”, Dynamical Systems, 2013, 1  crossref
    27. Kulczycki M., Kwietniak D., Oprocha P., “On Almost Specification and Average Shadowing Properties”, Fundam. Math., 224:3 (2014), 241–278  crossref  isi
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