On the Hausdorff measure of the Julia set and the escaping set of entire functions with regularly growing maximum modulus

DOI10.5186/AASFM.2017.4215zbMATH Open1375.37132OpenAlexW2588390735WikidataQ120769080 ScholiaQ120769080MaRDI QIDQ2965267

Jie Ding

Publication date: 2 March 2017

Published in: Annales Academiae Scientiarum Fennicae Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5186/aasfm.2017.4215

zbMATH Keywords

Julia setHausdorff measureexponential familygauge functionescaping set

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

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On the packing dimension of the Julia set and the escaping set of an entire function ⋮ Hausdorff measure of hairs without endpoints in the exponential family ⋮ Hausdorff measure of escaping and Julia sets for bounded-type functions of finite order ⋮ HOW POINTS ESCAPE TO INFINITY UNDER EXPONENTIAL MAPS

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