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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 5, Pages 1091–1115 (Mi izv2002)  

This article is cited in 42 scientific papers (total in 42 papers)

On small random perturbations of some smooth dynamical systems

Yu. I. Kifer


Abstract: This paper studies the problem of convergence of invariant measure which is a result of perturbation by a diffusion process with a small parameter (tending to zero) of certain smooth dynamical systems.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:5, 1083–1107

Bibliographic databases:

UDC: 517.9
MSC: Primary 58F15; Secondary 28A65, 60J60
Received: 21.11.1973

Citation: Yu. I. Kifer, “On small random perturbations of some smooth dynamical systems”, Izv. Akad. Nauk SSSR Ser. Mat., 38:5 (1974), 1091–1115; Math. USSR-Izv., 8:5 (1974), 1083–1107

Citation in format AMSBIB
\Bibitem{Kif74}
\by Yu.~I.~Kifer
\paper On small random perturbations of some smooth dynamical systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 5
\pages 1091--1115
\mathnet{http://mi.mathnet.ru/izv2002}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=388452}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 5
\pages 1083--1107
\crossref{https://doi.org/10.1070/IM1974v008n05ABEH002139}


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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. Yu. I. Kifer, “O malykh sluchainykh vozmuscheniyakh giperbolicheskikh predelnykh mnozhestv”, UMN, 32:1(193) (1977), 193–194  mathnet  mathscinet  zmath
    2. J. Guckenheimer, G. Oster, A. Ipaktchi, “The dynamics of density dependent population models”, J. Math. Biology, 4:2 (1977), 101  crossref
    3. David Ruelle, “Microscopic fluctuations and turbulence”, Physics Letters A, 72:2 (1979), 81  crossref
    4. Yuri Kifer, “On the principal eigenvalue in a singular perturbation problem with hyperbolic limit points and circles”, Journal of Differential Equations, 37:1 (1980), 108  crossref
    5. Yuri Kifer, “Stochastic stability of the topological pressure”, J. Anal. Math, 38:1 (1980), 255  crossref
    6. J. -P. Eckmann, “Roads to turbulence in dissipative dynamical systems”, Rev Mod Phys, 53:4 (1981), 643  crossref  mathscinet  zmath  adsnasa  isi
    7. Yuri Kifer, “The inverse problem for small random perturbations of dynamical systems”, Isr J Math, 40:2 (1981), 165  crossref  mathscinet  zmath  isi
    8. J -P Eckmann, L Thomas, P Wittwer, J Phys A Math Gen, 14:12 (1981), 3153  crossref  mathscinet  zmath  adsnasa
    9. J. P. Crutchfield, N. H. Packard, “Symbolic dynamics of one-dimensional maps: Entropies, finite precision, and noise”, Int J Theor Phys, 21:6-7 (1982), 433  crossref  mathscinet  zmath  isi
    10. J.P. Crutchfield, J.D. Farmer, B.A. Huberman, “Fluctuations and simple chaotic dynamics”, Physics Reports, 92:2 (1982), 45  crossref
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    12. J.P. Crutchfield, N.H. Packard, “Symbolic dynamics of noisy chaos”, Physica D: Nonlinear Phenomena, 7:1-3 (1983), 201  crossref
    13. Abraham Boyarsky, “On the significance of absolutely continuous invariant measures”, Physica D: Nonlinear Phenomena, 11:1-2 (1984), 130  crossref
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    21. Andrzej Lasota, Michael C Mackey, “Stochastic perturbation of dynamical systems: The weak convergence of measures”, Journal of Mathematical Analysis and Applications, 138:1 (1989), 232  crossref
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    24. R.S. MacKay, “An extension of Zeeman's notion of structural stability to non-invertible maps”, Physica D: Nonlinear Phenomena, 52:2-3 (1991), 246  crossref
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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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