Prog. Theor. Phys. Vol. 69 No. 5 (1983) pp. 1416-1426
Generalization of Baker's Transformation
— Chaos and Stochastic Process on a Smale's Horse-Shoe
Department of Physics, University of Kyoto, Kyoto 606
(Received December 16, 1982)
The area-preserving baker's transformation is extended in order to include the area non-preserving one, which is the model for a simple horse-shoe structure. The random motion on the horse-shoe is studied precisely, and the invariant density and the correlation function are obtained analytically and numerically.
The random walk on the horse-shoe structure is transformed into the generalized Brownian motion with the attractor, and the non-analytic density of the generalized baker's transformation is approximated by an analytic function. The topological similarity between the Lorenz chaos and the generalized baker's transformation is briefly discussed.
DOI : 10.1143/PTP.69.1416
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Citing Article(s) :
Progress of Theoretical Physics Supplement No.79 (1984) pp. 96-124
Statistical Mechanics of Intermittent Chaos
Yoji Aizawa, Chikara Murakami and Tamotsu Kohyama