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Title: On the connectivity of the escaping set for complex exponential Misiurewicz parameters
Author: Jarque i Ribera, Xavier
Keywords: Dinàmica
Funcions holomorfes
Dinàmica topològica
Holomorphic functions
Topological dynamics
Issue Date: 2011
Publisher: American Mathematical Society (AMS)
Abstract: 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.
Note: Reproducció del document publicat a:
It is part of: Proceedings of the American Mathematical Society, 2011, vol. 139, num. 6, p. 2057-2065
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ISSN: 0002-9939
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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