The maximal family of exactly solvable chaos
نویسنده
چکیده
A new two-parameter family of ergordic transformations with non-uniform invariant measures on the unit interval I = [0, 1] is found here. The family has a special property that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is also proven here that this family is the most generalized class of exactly solvable chaos on I including the Ulam=Neumann map y = 4x(1−x). Unpredictably, by choosing certain parameters, the maximal class of exactly solvable chaos is found to describe the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction. 05.45+b
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