Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.16202 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Motivated by the work of Boston, Jones and Goksel, we propose a Markov model for the factorisation of post-critically finite (PCF) cubic polynomials f. Using the information encoded in the critical orbits, we define a Markov model for PCF cubic polynomials with combined critical orbits of lengths one and two. Thanks to the work of Anderson et al., a complete list of PCF cubic polynomials over $\mathbb{Q}$ is available. Some of these polynomials have already been studied, such as those with colliding critical orbits analysed by Benedetto et al., which align with our model. We construct groups $M_n$ and prove that they follow our Markov model. These groups $M_n$ are conjectured to contain $\mathrm{Gal}(f^n)$.