On decomposable rational maps

TL;DR

This paper presents a uniformization theorem for decompositions of iterates of rational maps and proves the Fatou conjecture for decomposable rational maps, advancing understanding in complex dynamics.

Contribution

It introduces a uniformization theorem for the space of decompositions and confirms the Fatou conjecture specifically for decomposable rational maps.

Findings

Established a uniformization theorem for decompositions of rational map iterates.

Proved the Fatou conjecture for decomposable rational maps.

Enhanced understanding of the dynamics of decomposable rational maps.

Abstract

If $R$ is a rational map, the Main Result is a uniformization Theorem for the space of decompositions of the iterates of $R$. Secondly, we show that Fatou conjecture holds for decomposable rational maps.