Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 425-446

SEMI-HYPERBOLIC RATIONAL MAPS AND SIZE OF FATOU COMPONENTS

Dimitrios Ntalampekos

University of California, Los Angeles, Department of Mathematics
CA 90095, U.S.A.; dimitrisnt 'at' math.ucla.edu

Abstract. Recently, Merenkov and Sabitova introduced the notion of a homogeneous planar set. Using this notion they proved a result for Sierpinski carpet Julia sets of hyperbolic rational maps that relates the diameters of the peripheral circles to the Hausdorff dimension of the Julia set. We extend this theorem to Julia sets (not necessarily Sierpinski carpets) of semi-hyperbolic rational maps, and prove a stronger version of the theorem that was conjectured by Merenkov and Sabitova.

2010 Mathematics Subject Classification: Primary 37F10; Secondary 30C99.

Key words: Semi-hyperbolic, Hausdorff dimension, circle packings, homogeneous sets.

Reference to this article: D. Ntalampekos: Semi-hyperbolic rational maps and size of Fatou components. Ann. Acad. Sci. Fenn. Math. 43 (2018), 425-446.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4323