Joanna Horbaczewska

Dimension of the accumulation set of any hair for the exponential map

We study the dynamics of the exponential map on the complex plane. The set $\Lambda_{\mathbf{c}}$ of all points sharing a given itinerary $\mathbf{c}$ is non-empty if and only if $\mathbf{c}$ is an exponentially bounded itinerary. For such itineraries, $\Lambda_{\mathbf{c}}$ also contains a curve of escaping points, an...