Families of Commuting Formal Power Series and Formal Functional Equations |
Annales Mathematicae Silesianae 35 Issue 1, 55-76 (2020). DOI 10.2478/amsil-2020-0020
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.
GDPR | Families of Commuting Formal Power Series and Formal Functional Equations |