Geodesic
Concerning a stochastic dynamical system
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 803-809 
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/
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     title = {Concerning a stochastic dynamical system},
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     year = {1997},
     volume = {61},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Pikovski A. S., Feudel U., “Correlations and spectra of strange nonchaotic attractors”, J. Phys. A, 27 (1994), 5209–5219 | DOI

[2] Pikovski A. S., Feudel U., Kurths J., Zaks M. A., Singular continious spectra in dissipative dynamics. Nichtlineare Dynamik, Preprint, Max-Planck-Arbeitsgruppe, 1994, p. 1–25

[3] Oseledets V. I., “O spektre ergodicheskikh avtomorfizmov”, Dokl. AN SSSR, 168:5 (1968), 1009–1011

[4] Kornfeld I. P., Sinai Ya. G., Fomin S. P., Ergodicheskaya teoriya, Nauka, M., 1980 | Zbl

[5] Katok A. V., Stepin A. M., “Approksimatsii v ergodicheskoi teorii”, UMN, 22:5 (1967), 81–106 | MR | Zbl

[6] Ageev O. N., “Peremeshivanie v komponentakh perekladyvaniya $T_{\alpha,\beta}$”, UMN, 49:2 (1994), 143–144 | MR | Zbl