Computability and complexity of Julia sets: a review
Preprint Series # 1036
Kota, Hiratsuka and Yuzuru, Sato and Zin, Arai Computability and complexity of Julia sets: a review. (10 February 2014); (In Press)
Since A. M. Turing introduced the notion of computability
in 1936, various theories of real number computation have been
studied. 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.