1 results
Commuting rational functions revisited
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 41 / Issue 1 / January 2021
- Published online by Cambridge University Press:
- 15 August 2019, pp. 295-320
- Print publication:
- January 2021
-
- Article
- Export citation
-
Let
$B$ be a rational function of degree at least two that is neither a Lattès map nor conjugate to 
$z^{\pm n}$ or 
$\pm T_{n}$. We provide a method for describing the set 
$C_{B}$ consisting of all rational functions commuting with 
$B$. Specifically, we define an equivalence relation 
$\underset{B}{{\sim}}$ on 
$C_{B}$ such that the quotient 
$C_{B}/\underset{B}{{\sim}}$ possesses the structure of a finite group 
$G_{B}$, and describe generators of 
$G_{B}$ in terms of the fundamental group of a special graph associated with 
$B$.
