 This rule states, in other words, that if the entire infinite sequence begins with a certain initial value formula_76, then the lengths of the eras "k"(0), "k"(1), ..., are the numbers in the [[Continued fractions|continued fraction]] expansion

This expansion corresponds to the mapping transformation of the interval [0, 1] onto itself by the formula "Tx" = {1/"x"}, i.e., "x""s"+1 = {1/"x""s"}.This transformation belongs to the so-called expanding transformations of the interval [0, 1], i.e., transformations "x" → "f"("x") with |"f′"("x")| > 1.Such transformations possess the property of exponential instability