Hausdorff measure of Julia sets in the exponential family
Joern Peter
TL;DR
This paper investigates the Hausdorff measure of Julia and escaping sets of exponential maps, establishing conditions on gauge functions that determine whether these measures are zero or infinite.
Contribution
It provides new criteria linking gauge function growth to the measure properties of Julia and escaping sets in exponential dynamics.
Findings
Conditions for zero Hausdorff measure
Conditions for infinite Hausdorff measure
Insights into exponential map dynamics
Abstract
We consider the Hausdorff measure of Julia sets and escaping sets of exponential maps with respect to certain gauge functions. We give conditions on the growth of the gauge function which imply that the measure is zero or infinity, respectively.
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