In this talk, we present a surgery construction that replaces the interior dynamics in an orbit of wandering domains with the non-autonomous dynamics of a sequence of Blaschke products, as long as both are uniformly hyperbolic. The surgery is performed in infinitely many domains at once, despite mapping to each other with a degree larger than one. As an application, we construct an entire function with a wandering domain for which discrete and indiscrete grand orbit relations coexist, in a way that is not possible for periodic Fatou components. Understanding grand orbit relations in the different types of Fatou components is a key step in the study of quasiconformal deformations of holomorphic maps.

This is joint work with Vasiliki Evdoridou, Lukas Geyer and Leticia Pardo-Simon.