Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75432Let $ R $ be a rational map with totally disconnected Julia set $ J(R). $ If the postcritical set on $ J(R) $ contains a non-persistently recurrent (or conical) point, then we show that the map $ R $ can not be a structurally stable map.Dynamical Systems37F10 ;37F30Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia setstext