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A note on the Julia set of a rational function

Published online by Cambridge University Press:  24 October 2008

S. D. Letherman  and
R. M. W. Wood
S. D. Letherman
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL
R. M. W. Wood
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL
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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

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References

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