Geodesic
Concerning a stochastic dynamical system
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 803-809

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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. 
@article{MZM_1997_61_6_a0,
     author = {Z. I. Bezhaeva and V. I. Oseledets},
     title = {Concerning a stochastic dynamical system},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--809},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a0/}
}
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Z. I. Bezhaeva; V. I. Oseledets. Concerning a stochastic dynamical system. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 803-809. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a0/