Families of commuting formal power series and formal functional equations
Abstract
In this paper we describe families of commuting invertible formal power series in one indeterminate over ℂ, using the method of formal functional equations. We give a characterization of such families where the set of multipliers (first coefficients) σ of its members F(x) = σx+... is infinite, in particular of such families which are maximal with respect to inclusion, so called families of type I. The description of these families is based on Aczél–Jabotinsky differential equations, iteration groups, and on some results on normal forms of invertible series with respect to conjugation.
Keywords
commuting formal power series; maximal families of commuting formal power series; maximal abelian subgroups in $\Gamma$; formal functional equations; formal partial differential equations; Aczél–Jabotinsky equation; Briot–Bouquet equation; formal iteration groups of type I; ring of formal power series over $\mathbb{C}$
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Institute of Mathematics and Scientific Computing, University of Graz, Austria Austria
https://orcid.org/0000-0001-7449-8532
Institute of Mathematics and Scientific Computing, University of Graz, Austria Austria
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