15 research outputs found
Escape rate and Hausdorff measure for entire functions
Full text linkThe 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.Comment: 24 pages; some errors corrected, proof of Theorem 2 shortene
The size of Wiman-Valiron disks
Full text linkWiman-Valiron theory and results of Macintyre about "flat regions" describe
the asymptotic behavior of entire functions in certain disks around points of
maximum modulus. We estimate the size of these disks for Macintyre's theory
from above and below.Comment: 20 page
On buried points and phase transition points in the Julia sets concerning renormalization transformation
Get PDFOn limit functions and their natural boundaries in infinite compositions of entire functions
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