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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
\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
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 5
\pages 1083--1107

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    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
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    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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    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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    23. S. Yu. Dobrokhotov, V. N. Kolokoltsov, V. P. Maslov, “Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation $hu_t=h^2\Delta u/2-V(x)u$”, Theoret. and Math. Phys., 87:3 (1991), 561–599  mathnet  crossref  mathscinet  zmath  isi
    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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    38. E. A. Sataev, “Stokhasticheskie svoistva singulyarno giperbolicheskikh attraktorov”, Nelineinaya dinam., 6:1 (2010), 187–206  mathnet  elib
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