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Kneading theory of Lorenz maps. (English) Zbl 0701.58041

Dynamical systems and ergodic theory, 28th Sem. St. Banach Int. Math. Cent., Warsaw/Pol. 1986, Banach Cent. Publ. 23, 83-89 (1989).
[For the entire collection see Zbl 0686.00015.]
In the study of the geometrical model of the Lorenz attractor, a class of one-dimensional maps plays an important role. We refer to such maps as the Lorenz maps [see J. Guckenheimer and Ph. Holmes, “Nonlinear oscillations, dynamical systems, and bifurcations of vector fields” (1983; Zbl 0515.34001), C. Sparrow, “The Lorenz equations: bifurcations, chaos and strange attractors” (1982; Zbl 0504.58001), and F. Takens, Lect. Notes Math. 535, 237-253 (1976; Zbl 0354.34017)] although they are different from the one-dimensional maps presented by Lorenz [see E. N. Lorenz, J. Atmos. Sci. 20, 130- 141 (1963)]. We describe the use of the kneading theory to study the dynamics of Lorenz maps.

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure