Local connectivity of the Julia set of real polynomials

Abstract

In this paper we shall show that the Julia set of real polynomials of the form $f(z) = z^\ell+c_1$ with $\ell$ an even integer and $c_1$ real is either totally disconnected or locally connected. This answers a question of J. Milnor.

Authors

Genadi Levin

Sebastian van Strien