Escape rate and Hausdorff measure for entire functions
arXiv:1203.0190 · doi:10.1007/s00209-012-1085-x
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.
24 pages; some errors corrected, proof of Theorem 2 shortened
References in corpus (5)
- Dynamics of meromorphic functions with direct or logarithmic singularities
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- Hyperbolic dimension and radial Julia sets of transcendental functions
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Cited by in corpus (6)
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- The escaping set in transcendental dynamics
- On the dimension of the boundaries of attracting basins of entire maps
- Hausdorff dimension in quasiregular dynamics
- On the dimension of points which escape to infinity at given rate under exponential iteration
- On slow escaping and non-escaping points of quasimeromorphic mappings