Achievable connectivities of Fatou components for a family of singular perturbations

Jordi Canela, Xavier Jarque, Dan Paraschiv

Published 2021-02-01Version 1

In this paper we study the connectivity of Fatou components for maps in a large family of singular perturbations. We prove that, for some parameters inside the family, the dynamical planes for the corresponding maps present Fatou components of arbitrarily large connectivity and we determine precisely these connectivities. In particular, these results extend the ones obtained in [Can17, Can18].