Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1996-10-03
Phys. Rev. E 55(1997):5280-5284.
Nonlinear Sciences
Chaotic Dynamics
12 pages, 2 figures, REVTEX. Title was changed. Generalized Chebyshev maps including the precise form of two-parameter general
Scientific paper
10.1103/PhysRevE.55.5280
We present a new systematic method of constructing rational mappings as ergordic transformations with nonuniform invariant measures on the unit interval [0,1]. As a result, we obtain a two-parameter family of rational mappings that have a special property in that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is shown here that this family is the most generalized class of rational mappings possessing the property of exactly solvable chaos on the unit interval, including the Ulam=Neumann map y=4x(1-x). Based on the present method, we can produce a series of rational mappings resembling the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction, and we can match some rational functions with other experimentally obtained first return maps in a systematic manner.
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