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Predicting orbits of the Lorenz equation from symbolic dynamics. (English) Zbl 0925.58018
Summary: To a good approximation the family of maps proposed by Sparrow (1982) for the Lorenz system characterizes the dynamical behavior of the system very well. Such maps are numerically constructed. Symbolic dynamics of the maps is discussed. The procedures to find admissible sequences at given kneading sequences are proposed. By means of the symbolic dynamics allowed orbits are predicted for the Lorenz equation at a typical combination of parameters, and numerically located.

37E99Low-dimensional dynamical systems
37-99Dynamic systems and ergodic theory (MSC2000)
Full Text: DOI
[1] Lorenz, E. N.: J. atmos. Sci.. 20, 130 (1963)
[2] Sparrow, C.: The Lorenz equation: bifurcations, chaos, and strange attractors. (1982) · Zbl 0504.58001
[3] Guckenheimer, J.: Basel jguckenheimerjmosers.enewhouse dynamical systems. CTME lectures (1978)
[4] Collet, P.; Eckmann, J. P.: Iterated maps on the interval as dynamical systems. (1980) · Zbl 0458.58002
[5] Metropolis, N.; Stein, M. L.; Stein, P. R.: J. combin. Theory. 15, 25 (1973)
[6] Zheng, W. M.; Hao, B. L.: Intern. J. Mod. phys. B. 3, 1183 (1989)
[7] Zheng, W. M.; Liu, J. X.: Commun. theor. Phys.. 27, 423 (1997)