Hausdorff dimension of a dynamically defined set of exp(z)/z. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Zhan, Guo-Ping; Liu, Li-Han
• Is Part Of: Complex variables and elliptic equations. Volume 61:Issue 4(2016)
• Page Start: 469
• Page End: 483
• Publication Date: 2016-04-02
• Subjects: meromorphic function -- Hausdorff dimension -- escaping set; Primary: 30D05 -- Secondly: 37F10; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2015.1099158
• Languages: English
• ISSNs: 1747-6933

Abstract

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.