Fractional Iteration of Series and Transseries

Details Fractional Iteration of Series and Transseries Fractional Iteration of Series and Transseries

2010-02-11

arxiv.org/abs/1002.2378v1

Mathematics

Rings and Algebras

17 pages; 1 figure

Scientific paper

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 teration 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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