No invariant line fields on Cantor Julia sets

Abstract

In this paper, we prove that a rational map with a Cantor Julia set carries no invariant line fields on its Julia set. It follows that a structurally stable rational map with a Cantor Julia set is hyperbolic.

21 pages, 2 figures

References in corpus (2)

• Proof of the Branner-Hubbard conjucture on Cantor Julia sets
• Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets