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Mat. Zametki, 1997, Volume 61, Issue 6, Pages 803–809 (Mi mz1564)  

This article is cited in 1 scientific paper (total in 1 paper)

Concerning a stochastic dynamical system

Z. I. Bezhaevaa, V. I. Oseledetsb

a Moscow State Institute of Electronics and Mathematics
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study the discrete-time dynamical system
$$ X_{n+1}=2\sigma\cos(2\pi\theta_n)g(X_n),\qquad n\in\mathbb Z, $$
Where $\theta_n$ is an ergodic stationary process whose univariate distribution is uniform on the interval $[0,1]$, the function $g(x)$ is odd, bounded, increasing, and continuous, and $\mathbb Z$ is the ring of integers. It is proved that under certain conditions there exists a unique stationary process that is a solution of the above equation and this process has a continuous purely singular spectrum.

DOI: https://doi.org/10.4213/mzm1564

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English version:
Mathematical Notes, 1997, 61:6, 675–680

Bibliographic databases:

UDC: 519.21
Received: 04.05.1995

Citation: Z. I. Bezhaeva, V. I. Oseledets, “Concerning a stochastic dynamical system”, Mat. Zametki, 61:6 (1997), 803–809; Math. Notes, 61:6 (1997), 675–680

Citation in format AMSBIB
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\by Z.~I.~Bezhaeva, V.~I.~Oseledets
\paper Concerning a stochastic dynamical system
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 6
\pages 803--809
\mathnet{http://mi.mathnet.ru/mz1564}
\crossref{https://doi.org/10.4213/mzm1564}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629781}
\zmath{https://zbmath.org/?q=an:0915.58051}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 6
\pages 675--680
\crossref{https://doi.org/10.1007/BF02361208}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YE52200020}


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    This publication is cited in the following articles:
    1. Wang, XG, “Characterization of noise-induced strange nonchaotic attractors”, Physical Review E, 74:1 (2006), 016203  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
  • Математические заметки Mathematical Notes
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