Premium
Hausdorff Dimension and Hausdorff Measures of Julia Sets of Elliptic Functions
Author(s) -
Kotus Janina,
Urbański Mariusz
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001686
Subject(s) - hausdorff dimension , mathematics , hausdorff measure , dimension function , mathematics subject classification , julia set , effective dimension , hausdorff space , dimension (graph theory) , minkowski–bouligand dimension , multiplicity (mathematics) , packing dimension , pure mathematics , combinatorics , mathematical analysis , fractal dimension , fractal
It is proved here that if f : C → C ¯is an elliptic function and q is the maximal multiplicity of all poles of f , then the Hausdorff dimension of the Julia set of f is greater than 2 q /( q + 1), and the Hausdorff dimension of the set of points that escape to infinity is less than or equal to 2 q /( q + 1). In particular, the area of this latter set is equal to 0. 2000 Mathematics Subject Classification 37F35 (primary); 37F10, 30D30 (secondary).
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom