 This equation has a solution
(normalized to unity and taken to the first order of "x").In order for the "s"-th era to have a length "k", the preceding era must terminate with a number "x" in the interval between 1/("k" + 1) and 1/"k".Therefore, the probability that the era will have a length "k" is equal to (in the stationary limit)
At large values of "k"
In relating the statistical properties of the cosmological model with the [[Ergodicity|ergodic]] properties of the transformation "x""s"+1 = {1/"x""s"} an important point must be mentioned.