On the connectivity of the escaping set for complex exponential Misiurewicz parameters

الأصل · EN

Let E(z)= exp(z), λ∈ 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, the set of points in C with orbit tending to infinity is called the escaping set. We prove that the escaping set of E with Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.