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Two-Dimensional Chaos: The Baker Map Under Control

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Abstract

Some results on the stochastic control of a two-dimensional chaotic map, namely, the baker map, are presented. The approach is based on the probabilistic coupling of the controlled dynamics with a controlling system and the subsequent lifting of the coupled dynamics to a suitable functional space. The lifted dynamics is described in terms of probability densities and is governed by the linear Perron-Frobenius and Koopman operators. We obtain a sufficient condition for controllability and an estimation for the time to achieve control for a given accuracy in terms of the spectral decomposition of the Perron-Frobenius operator. Bibliography: 8 titles.

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Authors and Affiliations

  1. Laboratory of Complex Systems Theory, Institute for Physics, St. Petersburg, Russia

    Yu. A. Kuperin & D. A. Pyatkin

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  1. Yu. A. Kuperin
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  2. D. A. Pyatkin
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 206–214

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Kuperin, Y.A., Pyatkin, D.A. Two-Dimensional Chaos: The Baker Map Under Control. J Math Sci 128, 2798–2802 (2005). https://doi.org/10.1007/s10958-005-0234-8

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  • DOI: https://doi.org/10.1007/s10958-005-0234-8

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