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On the coarse coding of chaotic dynamics. (English. Russian original) Zbl 1106.37001
Probl. Inf. Transm. 42, No. 1, 64-68 (2006); translation from Probl. Peredachi Inf. 42, No. 1, 72-77 (2006).
The goal of this note is to demonstrate that under weak assumption on a deterministic dynamical system (weak mixing condition), there is a fundamental constraint on elementwise differences among codes corresponding to different trajectories.

37A05 Dynamical aspects of measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
37B10 Symbolic dynamics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI
[1] Bowen, R. Metody simvolicheskoi dinamiki (Methods of Symbolic Dynamics), Moscow: Mir, 1979.
[2] Kornfel’d, E.P., Sinai, Ya.G., and Fomin S.V., Ergodicheskaya teoriya, Moscow: Nauka, 1980. Translated under the title Ergodic Theory, New York: Springer, 1982.
[3] Blank, M. and Keller, G., Random Perturbations of Chaotic Dynamical Systems: Stability of the Spectrum, Nonlinearity, 1998, vol. 11, no. 5, pp. 1351–1364. · Zbl 0921.58051 · doi:10.1088/0951-7715/11/5/010
[4] Blank M., Ustoichivost’ i lokalizatsiya v khaoticheskoi dinamike (Stability and Localization in Chaotic Dynamics), Moscow: MCCME, 2001.
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