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Fractional iteration of series and transseries


Author: G. A. Edgar
Journal: Trans. Amer. Math. Soc. 365 (2013), 5805-5832
MSC (2010): Primary 03C64; Secondary 41A60, 39B12, 30B10
DOI: https://doi.org/10.1090/S0002-9947-2013-05784-4
Published electronically: July 10, 2013
MathSciNet review: 3091266
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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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Additional Information

G. A. Edgar
Affiliation: Department of Mathematics, The Ohio State University, 231 West Eighteenth Avenue, Columbus, Ohio 43210
Email: edgar@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0002-9947-2013-05784-4
Received by editor(s): February 25, 2010
Received by editor(s) in revised form: December 29, 2011
Published electronically: July 10, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.