Dept. Math, Hokkaido Univ. EPrints Server

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)

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Abstract

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.

Item Type:Preprint
Uncontrolled Keywords:Computability, Complexity, Julia sets, Turing machines, Complex dynamical systems
Subjects:03-xx MATHEMATICAL LOGIC AND FOUNDATIONS
68-xx COMPUTER SCIENCE
37-xx DYNAMICAL SYSTEMS AND ERGODIC THEORY
ID Code:2339