Geodesic
Functional equations in formal power series
Fedor Pakovich1
1Ben Gurion University of the Negev, Department of Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 601–620

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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 $z^2k[[z]]$ 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 $z^2k[[z]]$ is conjugate to a subsemigroup of the semigroup of monomials.
DOI : 10.54330/afm.149373
Keywords: Functional equations, formal power series, Böttcher's equation, semigroup amenability

Fedor Pakovich  1

1 Ben Gurion University of the Negev, Department of Mathematics 
Fedor Pakovich. Functional equations in formal power series. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 601–620. doi: 10.54330/afm.149373
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