Computability of the Julia set. Nonrecurrent critical orbits

TL;DR

This paper proves that the Julia set of certain rational functions can be computed efficiently in polynomial time under specific conditions related to the postcritical set.

Contribution

It establishes polynomial-time computability of Julia sets for rational functions with postcritical sets free of critical points or parabolic orbits.

Findings

Julia sets are computable in polynomial time under the given conditions.

The result applies to rational functions with nonrecurrent critical orbits.

Computability depends on the structure of the postcritical set.

Abstract

We prove that the Julia set of a rational function $f$ is computable in polynomial time, assuming that the postcritical set of $f$ does not contain any critical points or parabolic periodic orbits.