Hausdorff dimension of a dynamically defined set of exp(z)/z. Issue 4 (2nd April 2016) - Zhan, Guo-Ping; Liu, Li-Han
Abstract : Let for each . It was proved that the set, which consists of all points whose -limit set with respect to the map F is not the set, has zero Lebesgue measure. In this article, we apply some inequalities in conformal geometry to estimate area and diameter of planar sets and show that the set has Hausdorff dimension two. This implies the Hausdorff dimension of differs from its topological dimension, thus is a fractal set.