Almost every real quadratic polynomial has a poly-time computable Julia set

TL;DR

This paper proves that for a broad class of rational maps, including almost all real quadratic polynomials, their Julia sets can be computed efficiently in polynomial time, advancing understanding of computational complexity in dynamical systems.

Contribution

It establishes that Collet-Eckmann rational maps have polynomial-time computable Julia sets, showing that almost all real quadratic Julia sets are also poly-time computable.

Findings

Collet-Eckmann rational maps have poly-time computable Julia sets

Almost all real quadratic Julia sets are poly-time

Provides a complexity classification for Julia sets of broad map classes

Abstract

We prove that Collet-Eckmann rational maps have poly-time computable Julia sets. As a consequence, almost all real quadratic Julia sets are poly-time.