Geodesic
Two-dimensional chaos: the baker map under control
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 206-214 
Yu. A. Kuperin; D. A. Pyatkin. Two-dimensional chaos: the baker map under control. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 206-214. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a19/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Some results on the stochastic control of two-dimensional chaotic map, i.e., baker map are presented. The approach is based on probabilistic coupling of the controlled dynamics with a controlling system and subsequent lift of the coupled dynamics in a suitable functional space. The lifted dynamics is described in terms of probability densities and is governed by linear Perron–Frobenius and Koopman operators.

[1] A. Lasota, M. Mackey, Probabilistic Properties of Deterministic Systems, Cambrige University Press, NY, 1985 | MR | Zbl

[2] E. Ott, C. Grebogi, J. A. Yorke, “Controlling chaotic dynamical systems”, Chaos Soviet-American Perspectives on Nonlinear Science, ed. D. K. Campbell, American Institute of Physics, NY, 1990, 153–172 | MR

[3] Hiroshi H. Hasegawa, Dean J. Driebe, “Intrinsic irreversibility and the validity of the kinetic description of chaotic systems”, Phys. Rev. E, 50 (1994), 1781–1809 | DOI | MR

[4] Hiroshi H. Hasegawa, William C. Saphir, “Unitarity and irreversibility in chaotic systems”, Phys. Rev. A, 46 (1992), 7401–7423 | DOI | MR

[5] I. Antoniou, S. Tasaki, “Generalized spectral decomposition of mixing dynamical systems”, Intern. J. of Quantum Chemistry, 46 (1993), 425–474 | DOI

[6] I. Antoniou, V. Basios, F. Bosco, “Probabilistic Control of Chaos: Chaotic Maps Under Control.”, Computers Math. Applic., 34:2–4 (1997), 373–389 | DOI | MR | Zbl

[7] C. Obcema, E. Brandas, Ann. Phys., 151 (1983), 383 | DOI

[8] H. G. Schuster, Deterministic Chaos, Physik-Verlag, Weinheim, 1984 | MR | Zbl