A note on the Julia set of a rational function
Published online by Cambridge University Press: 24 October 2008
Extract
The purpose of this note is to present a few facts about the Julia set of a rational function that are well known to the experts in the subject of complex dynamics but whose documented exposition in the literature seems to need a little clarification. For example, under conditions set out in Theorem 1, the Julia set of a rational function can be expressed as the limit of a sequence of finite sets. In particular, for certain choices of a point α, the Julia set is the limit as n increases of the inverse image sets R−n(α). This formulation is widely exploited in the backwards iteration algorithm to produce computer illustrations of Julia sets (see for example Section 5·4 of [14]).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 3 , November 1995 , pp. 477 - 485
- Copyright
- Copyright © Cambridge Philosophical Society 1995
References
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