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30d30 (secondary)

Bulletin of the London Mathematical Society (1)

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HAUSDORFF DIMENSION AND HAUSDORFF MEASURES OF JULIA SETS OF ELLIPTIC FUNCTIONS
JANINA KOTUS, MARIUSZ URBAŃSKI
Journal:

Bulletin of the London Mathematical Society / Volume 35 / Issue 2 / March 2003

Published online by Cambridge University Press:

20 March 2003, pp. 269-275

Print publication:

March 2003
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It is proved here that if $f : {\rm C\!\!\!I} \rightarrow \bar{{\rm C\!\!\!I}}$ is an elliptic function and $q$ is the maximal multiplicity of all poles of $f$, then the Hausdorff dimension of the Julia set of $f$ is greater than $2q/(q+1)$, and the Hausdorff dimension of the set of points that escape to infinity is less than or equal to $2q/(q+1)$. In particular, the area of this latter set is equal to 0.