Asymptotics of Transversality in Periodic Curves of Quadratic Rational Maps

TL;DR

This paper calculates the Euler characteristic of the moduli space of quadratic rational maps with a specific periodic critical point, providing insights into the structure of these dynamical systems.

Contribution

It offers a novel computation of the Euler characteristic for the moduli space of quadratic rational maps with a periodic critical point.

Findings

Euler characteristic of the moduli space computed

Results contribute to understanding the topology of dynamical moduli spaces

Provides a foundation for further topological and dynamical studies

Abstract

We compute the Euler characteristic of the moduli space of quadratic rational maps with a periodic marked critical point of a given period.