# Dynamical Belyi maps

## TL;DR

This paper investigates rational maps with three ramification points, constructing infinite families of conservative maps and analyzing their reduction properties to gain insights into their rational dynamics.

## Contribution

It introduces new families of conservative rational maps with three ramification points, answering Silverman's question and providing detailed reduction analysis.

## Key findings

- Constructed infinitely many conservative maps of degree d.
- Provided strong reduction-based insights into rational dynamics.
- Answered a question posed by Silverman.

## Abstract

We study the dynamical properties of a large class of rational maps with exactly three ramification points. By constructing families of such maps, we obtain infinitely many conservative maps of degree $d$; this answers a question of Silverman. Rather precise results on the reduction of these maps yield strong information on the rational dynamics.