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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/51504
On the connectivity of the escaping set for complex exponential Misiurewicz parameters
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Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.
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JARQUE I RIBERA, Xavier. On the connectivity of the escaping set for complex exponential Misiurewicz parameters. Proceedings of the American Mathematical Society. 2011. Vol. 139, num. 6, pags. 2057-2065. ISSN 0002-9939. [consulted: 13 of June of 2026]. Available at: https://hdl.handle.net/2445/51504