Functional equations in formal power series

2022/08/17 by Fedor Pakovich, Pakovich, Fedor
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2208.08365

openalex publication_date 2022/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of characteristic zero, and k[[z]] the ring of formal power series over k. In this paper, we study equations in the semigroup z²k[[z]] with the semigroup operation being composition. We prove a number of general results about such equations and provide some applications. In particular, we answer a question of Horwitz and Rubel about decompositions of ``even'' formal power series. We also show that every right amenable subsemigroup of z²k[[z]] is conjugate to a subsemigroup of the semigroup of monomials.

Related

• Right amenability in semigroups of formal power series
• About the algebraic closure of formal power series in several variables
• Bases of subalgebras of K[[x]] and K[x]
• Elements of Finite Order in the Group of Formal Power Series Under Composition
• Semigroup associated with a free polynomial