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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/



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