Variations of Hausdorff Dimension in the Exponential Family

Guillaume Havard, Mariusz Urbanski, Michel Zinsmeister

In this paper we deal with the following family of exponential maps $(f_{\lambda }:z\mapsto \lambda (e^z-1){)}_{\lambda \in [1,+\infty )}$. Denoting $d(\lambda )$ the hyperbolic dimension of $f_{\lambda }$. It is known tha…