Two-Dimensional Chaos: The Baker Map Under Control

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.