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arXiv:1203.0190 [math.DS]AbstractReferencesReviewsResources

Escape rate and Hausdorff measure for entire functions

Walter Bergweiler, Jörn Peter

Published 2012-03-01, updated 2012-10-19Version 2

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.

Comments: 24 pages; some errors corrected, proof of Theorem 2 shortened
Journal: Math. Z. 274 (2013), 551-572
Categories: math.DS, math.CV
Subjects: 30D05, 37F10, 30D15
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