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On the connectivity of the escaping set for complex exponential Misiurewicz parameters
Jarque i Ribera, Xavier
Universitat de Barcelona
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.
Dinàmica
Funcions holomorfes
Dinàmica topològica
Dynamics
Holomorphic functions
Topological dynamics
(c) American Mathematical Society (AMS), 2011
Artículo
info:eu-repo/semantics/publishedVersion
American Mathematical Society (AMS)
         

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