Fractional iteration of series and transseries
Gerald A. Edgar · Transactions of the American Mathematical Society · 2013
We investigate compositional iteration of fractional order for transseries. For any large positive transseries T T of exponentiality 0 0 , there is a family T [ s ] T^{[s]} indexed by real numbers s s corresponding to iteration of order s s . It is based on Abel’s Equation. We also investigate the question of whether there is a family T [ s ] T^{[s]} all sharing a single support set. A subset of the transseries of exponentiality 0 0 is divided into three classes (“shallow”, “moderate” and “deep”) with different properties related to fractional iteration.