Abstract
An ordering for the parameter space of unimodal maps is proposed, based on characteristics similar to the winding number of circle maps. Sequences of rational approximants to the irrational values of this number may be viewed as scenarios of m-tuplings with non-integer m. Numerical and renormalization estimates show that in these scenarios geometric growth of the period is accompanied by double-exponential shrinking of scales in the parameter space and on the x-axis.
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