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Self-stochasticity phenomenon in dynamical systems generated by difference equations with continuous argument

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Abstract

For dynamical systems generated by the difference equations x(t+1) = f(x(t)) with continuous time (f is a continuous mapping of an interval onto itself), we present a mathematical substantiation of the self-stochasticity phenomenon, according to which an attractor of a deterministic system contains random functions.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    O. Yu. Romanenko

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  1. O. Yu. Romanenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 7, pp. 954–975, July, 2006.

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Romanenko, O.Y. Self-stochasticity phenomenon in dynamical systems generated by difference equations with continuous argument. Ukr Math J 58, 1079–1105 (2006). https://doi.org/10.1007/s11253-006-0122-5

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  • DOI: https://doi.org/10.1007/s11253-006-0122-5

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