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Mathematics of the USSR-Izvestiya, 1974, Volume 8, Issue 5, Pages 1083–1107
DOI: https://doi.org/10.1070/IM1974v008n05ABEH002139
(Mi im2002)
 

This article is cited in 65 scientific papers (total in 65 papers)

On small random perturbations of some smooth dynamical systems

Yu. I. Kifer
References:
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.
Received: 21.11.1973
Bibliographic databases:
UDC: 517.9
MSC: Primary 58F15; Secondary 28A65, 60J60
Language: English
Original paper language: Russian
Citation: Yu. I. Kifer, “On small random perturbations of some smooth dynamical systems”, 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 Math. USSR-Izv.
\yr 1974
\vol 8
\issue 5
\pages 1083--1107
\mathnet{http://mi.mathnet.ru/eng/im2002}
\crossref{https://doi.org/10.1070/IM1974v008n05ABEH002139}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=388452}
Linking options:
  • https://www.mathnet.ru/eng/im2002
  • https://doi.org/10.1070/IM1974v008n05ABEH002139
  • https://www.mathnet.ru/eng/im/v38/i5/p1091
  • This publication is cited in the following 65 articles:
    1. Cesar Maldonado, Hugo Nieto Loredo, “Annealed central limit theorem for a class of contractive random dynamical systems”, Journal of Difference Equations and Applications, 2024, 1  crossref
    2. Sumith Reddy Anugu, Vivek S. Borkar, “A Selection Procedure for Extracting the Unique Feller Weak Solution of Degenerate Diffusions”, Appl Math Optim, 87:3 (2023)  crossref
    3. Stefano Galatolo, Hugo Marsan, “Quadratic response and speed of convergence of invariant measures in the zero-noise limit”, DCDS, 41:11 (2021), 5303  crossref
    4. Harry Crimmins, Gary Froyland, “Fourier approximation of the statistical properties of Anosov maps on tori”, Nonlinearity, 33:11 (2020), 6244  crossref
    5. F. Cipriano, H. Ouerdiane, R. Vilela Mendes, “Stochastic stability of invariant measures: The 2D Euler equation”, Int. J. Mod. Phys. B, 33:17 (2019), 1950185  crossref
    6. Eleonora Catsigeras, Springer Proceedings in Mathematics & Statistics, 285, New Trends in One-Dimensional Dynamics, 2019, 113  crossref
    7. G. R. Ivanitskii, A. A. Deev, E. P. Khizhnyak, “Long-term dynamic structural memory in water: can it exist?”, Phys. Usp., 57:1 (2014), 37–65  mathnet  crossref  crossref  adsnasa  isi  elib
    8. Lai-Sang Young, “Mathematical theory of Lyapunov exponents”, J. Phys. A: Math. Theor, 46:25 (2013), 254001  crossref
    9. Lozi Mappings, 2013, 263  crossref
    10. Sergey P. Kuznetsov, Hyperbolic Chaos, 2012, 3  crossref
    11. S. P. Kuznetsov, “Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics”, Phys. Usp., 54:2 (2011), 119–144  mathnet  crossref  crossref  adsnasa  isi  elib
    12. Mei Zhu, Duo Wang, Maozheng Guo, “Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends”, Journal of Economic Dynamics and Control, 35:1 (2011), 131  crossref
    13. E. A. Sataev, “Stokhasticheskie svoistva singulyarno giperbolicheskikh attraktorov”, Nelineinaya dinam., 6:1 (2010), 187–206  mathnet  elib
    14. P Duarte, M J Torres, “Spectral stability of Markov systems”, Nonlinearity, 21:3 (2008), 381  crossref  mathscinet  zmath  isi
    15. Alexey Yu. Jalnine, Sergey P. Kuznetsov, “Effect of noise in a nonautonomous system of alternately excited oscillators with a hyperbolic strange attractor”, Phys Rev E, 77:3 (2008), 036220  crossref  isi
    16. R. Vilela Mendes, “Network Dynamics: Tools and Examples”, Nonlinear Dyn, 44:1-4 (2006), 181  crossref  mathscinet  zmath  isi
    17. Yuri Kifer, Pei-Dong Liu, Handbook of Dynamical Systems, 1, 2006, 379  crossref
    18. Springer Series in Synergetics, 15, Noise-Induced Transitions, 2006, 201  crossref
    19. V. S. Anishchenko, T. E. Vadivasova, G. A. Okrokvertskhov, G. I. Strelkova, “Statistical properties of dynamical chaos”, Phys. Usp., 48:2 (2005), 151–166  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    20. R. VILELA MENDES, “TOOLS FOR NETWORK DYNAMICS”, Int. J. Bifurcation Chaos, 15:04 (2005), 1185  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:636
    Russian version PDF:173
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    References:91
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