<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we describe families of commuting invertible formal power series in one indeterminate over ℂ, using the method of <italic>formal functional</italic> equations. We give a characterization of such families where the set of multipliers (first coefficients) <italic>σ</italic> of its members <italic>F</italic> (<italic>x</italic>) = <italic>σx</italic> + . . . is infinite, in particular of such families which are maximal with respect to inclusion, so called families of <italic>type I</italic>. 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.</p></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.

Families of Commuting Formal Power Series and Formal Functional Equations

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Families of Commuting Formal Power Series and Formal Functional Equations"}

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...

Families of Commuting Formal Power Series and Formal Functional Equations

Published Online: Oct 06, 2020

Page range: 55 - 76

Received: May 20, 2020

Accepted: Aug 19, 2020

DOI: https://doi.org/10.2478/amsil-2020-0020

© 2020 Harald Fripertinger et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.