Julia set of the function \(z\exp(z+\mu)\) (Q1312834)

The author shows that there is a certain \(\alpha> 2\) such that for all \(\mu\in (-\infty,2)\cup (2,\alpha)\) the function \(f_ \mu\): \(z\to z \exp(z+\mu)\) has a Julia set which is not the whole complex plane. He also shows that there is a sequence \(\mu_ n\) such that \(2< \mu_ n< \mu_{n+1}\) and the Julia set of \(f_{\mu_ n}\) is the whole complex plane.