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Home  >  Volume 26 (March 2014)

11. On Rational Maps Whose Julia Set Is The Entire Complex Sphere by K. B. Yuguda. Volume26, (March, 2014), pp 54 – 57.
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Abstract

In this paper, following closely the technique of Ritt, we showed that for a class of rational maps, the Julia Set is the entire complex sphere. This is achieved by the use of a group of translations with two generators which makes it fairly easy to analyze the behavior of their iterates and of course, coupled with powerful techniques in complex analysis. Intuitively, if the Julia Set of a given set in this context is the entire complex sphere, then its Fatou Set is empty. 

Keywords:equicontinuity, Fatou set, Julia set,  lattice, period parallelogram, elliptic function.

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