Abstract:

We prove that the escaping set of $E$_&lambda(z)=&lambda e^z with Misiurewicz is a connected set. This fact and previous result in the literature seems to point out that having an asymptotic value, rather than a critical value, in the Julia set is the key ingredient for the connectedness of the escaping set. Recently, Lasse Rempe, has extended this result to other parameter values by using similar arguments.