Escape rate and Hausdorff measure for entire functions
Walter Bergweiler, J\"orn Peter
TL;DR
This paper investigates the size of subsets of the escaping set of entire functions, using Hausdorff measure and escape rates to establish bounds on their measure.
Contribution
It introduces bounds for the Hausdorff measure of escape rate-defined subsets of the escaping set of entire functions.
Findings
Established upper and lower bounds for Hausdorff measure of escape rate subsets
Connected escape rates with measure-theoretic properties of entire functions
Provided new insights into the geometric structure of escaping sets
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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