Univalent Baker domains (Q2722664)

Let \(f\) be an entire map and \(U\) be a periodic domain, \(f^p(U)\subset U\) for some \(p\). The domain \(U\) is called a Baker domain if \(f^{np}(z)\to\infty\) as \(n\to\infty\) for all \(z\in U\). The Baker domain is open and invariant. Assuming \(f|_U\) is univalent, the authors give a classification of corresponding Baker domains. Three cases are possible, depending on the behavior of backwards iterations. The paper also contains examples of Baker domains, including a domain with disconnected boundary in \(\mathbb C\) and a domain, which spirals towards infinity.