Bulletin of the London Mathematical Society · 2003 · 39 citations · 0 references
Natural SciencesMathematicsGeometrySet TheoryTopologyAlgebraic GeometryArithmetic GeometryElliptic CurvesFractal GeometryMetric GeometryElliptic FunctionsJulia SetsRiemann - Roch Theory
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 2q/(q + 1). In particular, the area of this latter set is equal to 0. 2000 Mathematics Subject Classification 37F35 (primary); 37F10, 30D30 (secondary).