# On the connectivity of the escaping set for complex exponential Misiurewicz parameters - Mathematics > Dynamical Systems

On the connectivity of the escaping set for complex exponential Misiurewicz parameters - Mathematics > Dynamical Systems - Download this document for free, or read online. Document in PDF available to download.

Abstract: Let $E {\la}z=\la { m exp}z, \ \lambda\in \mathbb C$ be the complexexponential family. For all functions in the family there is a uniqueasymptotic value at 0 and no critical values. For a fixed $\la$, the set ofpoints in $\mathbb C$ with orbit tending to infinity is called the escapingset. We prove that the escaping set of $E {\la}$ with $\la$ Misiurewicz thatis, a parameter for which the orbit of the singular value is strictlypreperiodic is a connected set.

Author: ** Xavier Jarque**

Source: https://arxiv.org/