Year: 2025
Type: article
Abstract: Let F be a rational function of one complex variable of degree m ≥ 2. The function F is called simple if for every z ∈ ℂℙ1 the preimage F −1{z} contains at least m − 1 points. We show that if F is a simple rational function of degree m ≥ 4 and F ◦l = G r ◦ G r−1 ◦ ⋯ ◦ G 1, l ≥ 1, is a decomposition of an iterate of F into a composition of indecomposable rational functions, then r = l and there exist Möbius transformations μ i , 1 ≤ i ≤ r − 1, such that G r = F ◦ μ r−1, G i = μ i −1 ◦ F ◦ μ i−1, 1 < i < r, and G 1 = μ 1 −1 ◦ F. As applications, we solve a number of problems in complex and arithmetic dynamics for “general” rational functions.
Source: Journal d Analyse Mathématique
Author: Fedor Pakovich
Institution: Ben-Gurion University of the Negev
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Israel Science Foundation
Award: G1573168548
OpenAlex ID: W3181608084