Fractional Iteration of Series and Transseries

G. A. Edgar

G. A. Edgar
Department of Mathematics
The Ohio State University
Columbus, OH 43210   U.S.A.


We investigate compositional iteration of fractional order for transseries. For any large positive transseries T of exponentiality 0, there is a family T[s] indexed by real numbers s corresponding to iteration of order s. It is based on Abel's Equation. We also investigate the question of whether there is a family T[s] all sharing a single support set. A subset of the transseries of exponentiality 0 is divided into three classes ("shallow", "moderate" and "deep") with different properties related to fractional iteration.

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