Abstract
The escaping set of an entire function is the set of points that tend to infinity under iteration. We consider subsets of the escaping set defined in terms of escape rates and obtain upper and lower bounds for the Hausdorff measure of these sets with respect to certain gauge functions.
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Acknowledgments
We thank Lasse Rempe and the referee for a great number of very helpful comments and suggestions.
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Both authors are supported by the Deutsche Forschungsgemeinschaft, grant no. Be 1508/7-2.
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Bergweiler, W., Peter, J. Escape rate and Hausdorff measure for entire functions. Math. Z. 274, 551–572 (2013). https://doi.org/10.1007/s00209-012-1085-x
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DOI: https://doi.org/10.1007/s00209-012-1085-x