Fractional iteration of series and transseries

Edgar, G.

doi:10.1090/S0002-9947-2013-05784-4

Fractional iteration of series and transseries
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by G. A. Edgar PDF

Trans. Amer. Math. Soc. 365 (2013), 5805-5832 Request permission

Abstract:

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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