Abstract

... Although the hyperbolic Julia sets were shown to be recursive, complexity bounds were proven only for a restricted case in [13]. Our paper is a significant generalization of [13], in which polynomial time computability was shown for a special kind of hyperbolic polynomials, namely, polynomials of the form p(z) = z2 + c with| c | < 1/4. We show that the machine drawing the Julia set can be made independent of the hyperbolic polynomial p, and provide some evidence suggesting that one cannot expect a much better computability result for Julia sets. We also introduce an alternative real set computability definition due to Ko, and show an interesting connection between this definition and the main definition.

Citations