For citation:
Golubencev A. F., Anikin V. M., Noyanova . A. Modifications of the baker transformation and their asimptotic properties. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 3, pp. 45-57. DOI: 10.18500/0869-6632-2004-12-3-45-57
Modifications of the baker transformation and their asimptotic properties
Some modifications of the baker transformation are introduced. The equations for the brunches of the maps are solved exactly. It is shown that the y-component of baker transformations is represented by a linear autoregression equation of the first order where digits of the initial value x₀, play the role of ап excitation (input signal) if x₀, is considered as а random value. It is shown that the digital filter corresponding to the baker transformation is causal, stable and reversible one. The asymptotic regime of baker transform dynamics does not depend оп the distribution of the initial value y₀,. Investigations of asymptotic properties of the baker map are important for chaos-based key cryptography schemes for digital communication.
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