# Transversality for critical relations of families of rational maps: an elementary proof

## TL;DR

This paper provides a simple and elementary proof demonstrating that critical relations in families of rational maps unfold transversally within the parameter space.

## Contribution

It offers a new, straightforward proof of transversality of critical relations in rational map families, simplifying previous approaches.

## Key findings

- Critical relations unfold transversally in rational map families.
- Elementary proof simplifies understanding of transversality.
- Supports further research in complex dynamics and bifurcation theory.

## Abstract

In this paper we will give a short and elementary proof that critical relations unfold transversally in the space of rational maps.