Computability and complexity of Julia sets: a review

Abstract

Since A. M. Turing introduced the notion of computability in 1936, various theories of real number computation have been studied [1,10,13]. Some are of interest in nonlinear and statistical physics while others are extensions of the mathematical theory of computation. In this review paper, we introduce a recently developed computability theory for Julia sets in complex dynamical systems by Braverman and Yampolsky [3].