G. A. Edgar Department of Mathematics The Ohio State University Columbus, OH 43210 U.S.A.edgar@math.ohio-state.edu |

## AbstractWe investigate compositional iteration of fractional order for transseries. For any large positive transseriesT
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.
fractional.pdf (version of December, 2011) |